Let X and Y be two independent and identically distributed random variables that take only positive integer values. Their PMF is px (n) = py (n) = 2^-n for every n e N, where N is the set of positive

20,695 results
  1. statistics

    Let 𝑋 and π‘Œ be independent positive random variables. Let 𝑍=𝑋/π‘Œ. In what follows, all occurrences of π‘₯, 𝑦, 𝑧 are assumed to be positive numbers. 1. Suppose that 𝑋 and π‘Œ are discrete, with known PMFs, 𝑝𝑋 and π‘π‘Œ.

  2. Statistics and Probability

    Let N be a random variable with mean E[N]=m, and Var(N)=v; let A1, A2,… be a sequence of i.i.d random variables, all independent of N, with mean 1 and variance 1; let B1,B2,… be another sequence of i.i.d. random variables, all independent of N and of

  3. Probability

    Let X and Y be independent positive random variables. Let Z=X/Y . In what follows, all occurrences of x , y , z are assumed to be positive numbers. 1) Suppose that X and Y are discrete, with known PMFs, pX and pY . Then, pZ|Y(z|y)=pX(?). What is the

  4. probability

    Let 𝑋 and π‘Œ be independent positive random variables. Let 𝑍=𝑋/π‘Œ . In what follows, all occurrences of π‘₯ , 𝑦 , 𝑧 are assumed to be positive numbers. 1. Suppose that 𝑋 and π‘Œ are discrete, with known PMFs, 𝑝𝑋 and π‘π‘Œ .

  5. probability

    For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between βˆ’1 and 1. Let Ui=X1+X2+β‹―+Xii,i=1,2,…. What value does the

  6. math

    Conditioned on the result of an unbiased coin flip, the random variables T1,T2,…,Tn are independent and identically distributed, each drawn from a common normal distribution with mean zero. If the result of the coin flip is Heads, this normal

  7. Math

    Searches related to The random variables X1,X2,…,Xn are continuous, independent, and distributed according to the Erlang PDF fX(x)=Ξ»3x2eβˆ’Ξ»x2, for xβ‰₯0, where Ξ» is an unknown parameter. Find the maximum likelihood estimate of Ξ» , based on observed

  8. math, probability

    Exercise: CLT applicability Consider the class average in an exam in a few different settings. In all cases, assume that we have a large class consisting of equally well prepared students. Think about the assumptions behind the central limit theorem, and

  9. maths

    Suppose that the random variables Θ and X are not independent, but E[Θ∣X=x]=3 for all x . Then the LLMS estimator of Θ based on X is of the form aX+b , with a= b=

  10. probability and statistics

    Let Θ1, Θ2, W1, and W2 be independent standard normal random variables. We obtain two observations, X1=Θ1+W1,X2=Θ1+Θ2+W2. Find the MAP estimate θ^=(θ^1,θ^2) of (Θ1,Θ2) if we observe that X1=1, X2=3. (You will have to solve a system of two linear

  11. Probability

    Convergence in probability. For each of the following sequences, determine whether it converges in probability to a constant. If it does, enter the value of the limit. If it does not, enter the number β€œ999". 1) Let X1, X2,… be independent continuous

  12. probability

    Let X and Y be independent positive random variables. Let Z=X/Y. In what follows, all occurrences of x, y, z are assumed to be positive numbers. 1) Suppose that X and Y are discrete, with known PMFs, p_X and p_Y. Then, pZ|Y(z|y)=pX(?). What is the argument

  13. Probability

    Maximum likelihood estimation The random variables X1,X2,…,Xn are continuous, independent, and distributed according to the Erlang PDF fX(x)= (Ξ»^3*x^2*e^(βˆ’Ξ»x))/2, for xβ‰₯0, where Ξ» is an unknown parameter. Find the maximum likelihood estimate of

  14. probability

    When you enter your bank, you find that there are only two tellers, both busy serving other customers, and that there are no other customers in line. Assume that the service times for you and for each of the customers being served are independent

  15. probability

    Let X and Y be independent Erlang random variables with common parameter Ξ» and of order m and n, respectively. Is the random variable X+Y Erlang? If yes, enter below its order in terms of m and n using standard notation. If not, enter 0.

  16. Probability & Statistics

    Exercise: Convergence in probability a) Suppose that Xn is an exponential random variable with parameter Ξ»=n. Does the sequence {Xn} converge in probability? b) Suppose that Xn is an exponential random variable with parameter Ξ»=1/n. Does the sequence

  17. Probability

    For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,… be independent continuous random variables, each uniformly distributed between βˆ’1 and 1. Let Ui=X1+X2+β‹―+Xii,i=1,2,…. What value does the

  18. Probability & Statistics

    We saw that if we want to have a probability of at least 95% that the poll results are within 1 percentage point of the truth, Chebyshev's inequality recommends a sample size of n = 50,000. This is very large compared to what is done in practice. Newspaper

  19. probability

    This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and [0,1], respectively. At x=1, the value of the joint PDF is 1/2. (figure belongs to "the science of uncertainty) 1. Are X and Y

  20. probability

    t the discrete random variable X be uniform on {0,1,2} and let the discrete random variable Y be uniform on {3,4}. Assume that X and Y are independent. Find the PMF of X+Y using convolution. Determine the values of the constants a, b, c, and d that appear

  21. probability

    When you enter the bank, you find that there are only two tellers, both busy serving other customers, and that there are no other customers in queue. Assume that the service times for you and for each of the customers being served are independent

  22. Probability

    Suppose that we have three engines, which we turn on at time 0. Each engine will eventually fail, and we model each engine's lifetime as exponentially distributed with parameter Ξ». The lifetimes of different engines are independent. One of the engines

  23. math , probability

    Let X and Y be two independent and identically distributed random variables that take only positive integer values. Their PMF is px (n) = py (n) = 2^-n for every n e N, where N is the set of positive integers. 1. Fix at E N. Find the probability P

  24. Probability

    1. Suppose three random variables X , Y , Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z). Then, are X and Y independent given Z? 2.Suppose random variables X and Y are independent given Z , then the joint distribution must be of

  25. probability

    Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let 𝑋 and π‘Œ be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)π‘Œ . Find the probability 𝐏(ln𝐻β‰₯𝑧) where

  26. probability

    Maximum likelihood estimation The random variables X1,X2,…,Xn are continuous, independent, and distributed according to the Erlang PDF fX(x)=[Ξ»^3*x^2*e^(βˆ’Ξ»x)]/2, for xβ‰₯0, where Ξ» is an unknown parameter. Find the maximum likelihood estimate of Ξ»,

  27. Probability

    1.Let 𝑋 and π‘Œ be two binomial random variables: a.If 𝑋 and π‘Œ are independent, then 𝑋+π‘Œ is also a binomial random variable b.If 𝑋 and π‘Œ have the same parameters, 𝑛 and 𝑝 , then 𝑋+π‘Œ is a binomial random variable c.If 𝑋

  28. Probability

    The joint PMF, pX,Y(x,y), of the random variables X and Y is given by the following table: (see: the science of uncertainty) 1. Find the value of the constant c. c = 0.03571428571428571428 2. Find pX(1). pX(1)= 1/2 3. Consider the random variable Z=X2Y3.

  29. Probability

    Let X and Y be independently random variables, with X uniformly distributed on [0,1] and Y uniformly distributed on [0,2] . Find the PDF fZ(z) of Z=max{X,Y} 1. For z2 : find fZ(z) 2. For 0≀z≀1 : find fZ(z)

  30. Probability

    Let U, V, and W be independent standard normal random variables (that is, independent normal random variables, each with mean 0 and variance 1), and let X=3U+4V and Y=U+W. Give a numerical answer for each part below. You may want to refer to the standard

  31. Probability

    For each of the following statements, determine whether it is true (meaning, always true) or false (meaning, not always true). Here, we assume all random variables are discrete, and that all expectations are well-defined and finite. Let X and Y be two

  32. MATH URGENT!!!!

    An investigator was interested in studying the effect of taking a course in child development on attitudes toward childrearing. At the end of the semester, the researcher distributed a questionnaire to students who had taken the child development course.

  33. math, probability

    Let X and Y be independent random variables, uniformly distributed on [0,1] . Let U=min{X,Y} and V=max{X,Y} . Let a=E[UV] and b=E[V] 1. Find a 2. Find b 3. Find Cov(U,V) . You can give either a numerical answer or a symbolic expression involving a and b .

  34. Probability

    Suppose that we have a box that contains two coins: A fair coin: P(H)=P(T)=0.5 . A two-headed coin: P(H)=1 . A coin is chosen at random from the box, i.e. either coin is chosen with probability 1/2 , and tossed twice. Conditioned on the identity of the

  35. Probability

    The random variables X1,..,Xn are independent Poisson random variables with a common parameter Lambda . Find the maximum likelihood estimate of Lambda based on observed values x1,...,xn.

  36. Probability

    In the following problem, please select the correct answer. Let X be a non-negative random variable. Then, for any a>0, the Markov inequality takes the form P(Xβ‰₯a)≀(a^c)E[X^5]. What is the value of c? c= unanswered Suppose that X_1,X_2,β‹― are random

  37. Probability

    Suppose that we have a box that contains two coins: A fair coin: P(H)=P(T)=0.5 . A two-headed coin: P(H)=1 . A coin is chosen at random from the box, i.e. either coin is chosen with probability 1/2 , and tossed twice. Conditioned on the identity of the

  38. Probability

    Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variables Y1 =X1βˆ’X3, Y2 =X2βˆ’X3. We further introduce indicator random variables Zi∈{0,1} with Zi=1 if and only if Yi=0 for i=1,2 . Calculate

  39. Math

    Let 𝑋 and π‘Œ be independently random variables, with 𝑋 uniformly distributed on [0,1] and π‘Œ uniformly distributed on [0,2] . Find the PDF 𝑓𝑍(𝑧) of 𝑍=max{𝑋,π‘Œ} . For 𝑧2 : 𝑓𝑍(𝑧)= For 0≀𝑧≀1 : 𝑓𝑍(𝑧)= For

  40. Probability

    This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0,2] and [0,1], respectively. At x=1, the value of the joint PDF is 1/2. Are X and Y independent? - unanswered Yes No Find fX(x). Express your

  41. Probability

    Let N be a geometric r.v. with mean 1/p; let A1,A2,… be a sequence of i.i.d. random variables, all independent of N, with mean 1 and variance 1; let B1,B2,… be another sequence of i.i.d. random variable, all independent of N and of A1,A2,…, also with

  42. Probability

    Let X1 , X2 , X3 be i.i.d. Binomial random variables with parameters n=2 and p=1/2 . Define two new random variables Y1 =X1βˆ’X3, Y2 =X2βˆ’X3. We further introduce indicator random variables Zi∈{0,1} with Zi=1 if and only if Yi=0 for i=1,2 . 1. Calculate

  43. Probability

    Let N,X1,Y1,X2,Y2,… be independent random variables. The random variable N takes positive integer values and has mean a and variance r. The random variables Xi are independent and identically distributed with mean b and variance s, and the random

  44. math

    Let X1,X2,… be a sequence of independent random variables, uniformly distributed on [0,1] . Define Nn to be the smallest k such that X1+X2+β‹―+Xk exceeds cn=n2+n12βˆ’βˆ’βˆ’βˆš , namely, Nn = min{kβ‰₯1:X1+X2+β‹―+Xk>cn} Does the limit limnβ†’βˆžP(Nn>n)

  45. probability, mathematics, statistics

    Let A and B be independent random variables with means 1 , and variances 1 and 2 , respectively. Let X=Aβˆ’B and Y=A+B . Find the coefficients c1 and c2 of the Linear Least Mean Squares (LLMS) estimator YΛ†LLMS=c1X+c2 of Y based on X .

  46. Statistics & Probability

    When you enter your bank, you find that there are only two tellers, both busy serving other customers, and that there are no other customers in line. Assume that the service times for you and for each of the customers being served are independent

  47. probability

    Let X and Y be independent continuous random variables that are uniformly distributed on (0,1). Let H=(X+2)Y. Find the probability P(lnHβ‰₯z) where z is a given number that satisfies ez

  48. Math

    Let X and Y be independently random variables, with X uniformly distributed on [0,1] and Y uniformly distributed on [0,2] . Find the PDF fZ(z) of Z=max{X,Y} find fZ(z) 1. For z2 : 2. For 0≀z≀1 : 3. For 1≀z≀2 :

  49. probability

    et X and Y be independent Erlang random variables with common parameter Ξ» and of order m and n, respectively. Is the random variable X+Y Erlang? If yes, enter below its order in terms of m and n using standard notation. If not, enter 0.

  50. Probability

    Let N,X1,Y1,X2,Y2,… be independent random variables. The random variable N takes positive integer values and has mean a and variance r. The random variables Xi are independent and identically distributed with mean b and variance s, and the random

  51. arithmetic

    Assume you roll a fair dice twice. Two rolls are independent and identically distributed, with probability of rolling a particular number being 1/6. So, for instance, the probability of rolling 5 and then 2 is P(5,2) = P(5) β‹… P(2) = 1/6 β‹… 1/6 = 1/36

  52. probability

    Let 𝑋 and π‘Œ be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)π‘Œ . Find the probability 𝐏(ln𝐻β‰₯𝑧) where 𝑧 is a given number that satisfies 𝑒^𝑧

  53. Statistics

    In a population, heights of males are normally distributed with u=180 cm and sigma^2=16 cm^2, while the heights of females are normally distributed with u=170 cm and sigma^2= 25 cm^2. a) One random male and one random female are selected from the

  54. Maths Probability

    Let X and Y be independent random variables, each uniformly distributed on the interval [0,2]. Find the mean and variance of XY. E[XY]= 1 var[XY]= ??? Find the probability that XYβ‰₯1. Enter a numerical answer. P(XYβ‰₯1)= ???

  55. Probability

    Let U, V, and W be independent standard normal random variables (that is, independent normal random variables, each with mean 0 and variance 1), and let X=3U+4V and Y=U+W. Give a numerical answer for each part below. You may want to refer to the standard

  56. math, probability

    Let X1,X2,… be a sequence of independent random variables, uniformly distributed on [0,1] . Define Nn to be the smallest k such that X1+X2+β‹―+Xk exceeds cn=n2+n12βˆ’βˆ’βˆ’βˆš , namely, Nn = min{kβ‰₯1:X1+X2+β‹―+Xk>cn} Does the limit limnβ†’βˆžP(Nn>n)

  57. Probability

    For each of the following statements, state whether it is true (meaning, always true) or false (meaning, not always true): 1. Let X and Y be two binomial random variables. (a) If X and Y are independent, then X+Y is also a binomial random variable. (b) If

  58. math , probability

    Let 𝑋 and π‘Œ be independent random variables, uniformly distributed on [0,1]. Let π‘ˆ=min{𝑋,π‘Œ} and 𝑉=max{𝑋,π‘Œ}. Let π‘Ž=𝐄[π‘ˆπ‘‰] and 𝑏=𝐄[𝑉]. 1. Find π‘Ž. 2. Find 𝑏. 3. Find Cov(π‘ˆ,𝑉). You can give either a

  59. Statistics

    Let X and Y be independently random variables, with X uniformly distributed on [0,1] and Y uniformly distributed on [0,2] . Find the PDF fZ(z) of Z=max{X,Y} . For z2 : fZ(z)= For 0≀z≀1 : fZ(z)= For 1≀z≀2 : fZ(z)=

  60. probability

    If two random variables 𝑋 and π‘Œ are independent, which conclusion in the following is not true

  61. Maths

    Approximate the probability that the sum of the 16 independent uniform (0,1) random variables exceeds 10.

  62. Probability

    Let 𝐴 and 𝐡 be independent random variables with means 1, and variances 1 and 2, respectively. Let 𝑋=π΄βˆ’π΅ and π‘Œ=𝐴+𝐡. Find the coefficients 𝑐1 and 𝑐2 of the Linear Least Mean Squares (LLMS) estimator

  63. Statistics

    I neep help on two questions! A condition that occurs in multiple regression analysis if the independent variables are themselves correlated is known as: 1. autocorrelation 2. stepwise regression 3. multicorrelation 4. multicollinearity (I think this is

  64. probability

    Let N,X1,Y1,X2,Y2,… be independent random variables. The random variable N takes positive integer values and has mean a and variance r. The random variables Xi are independent and identically distributed with mean b and variance s, and the random

  65. probablity

    In this problem, you may find it useful to recall the following fact about Poisson random variables. Let X and Y be two independent Poisson random variables, with means Ξ»1 and Ξ»2, respectively. Then, X+Y is a Poisson random variable with mean Ξ»1+Ξ»2.

  66. probablity

    Let X and Y be two independent Poisson random variables, with means Ξ»1 and Ξ»2, respectively. Then, X+Y is a Poisson random variable with mean Ξ»1+Ξ»2. Arguing in a similar way, a Poisson random variable X with parameter t, where t is a positive integer,

  67. Probability

    Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter p∈(0,1). If X is even, then Y and Z are equal to zero. If X is odd, (Y,Z) is uniformly distributed on the set

  68. Statistics

    You would like to determine the percentage of coffee drinkers in your university, and collected the following binary data set from random students on campus, 1 for coffee drinker and 0 for otherwise: 0,0,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1. Let Yi

  69. statistics

    Let X be the average of a sample of size 25 independent normal random variables with mean 0 and variance 1. P[[X

  70. arithmetic

    Assume you roll a fair dice twice. Two rolls are independent and identically distributed, with probability of rolling a particular number being 1/6. So, for instance, the probability of rolling 5 and then 2 is P(5,2) = P(5) β‹… P(2) = 1/6 β‹… 1/6 = 1/36

  71. probability

    1) Let X and Y be independent continuous random variables that are uniformly distributed on (0,1) . Let H=(X+2)Y . Find the probability P(lnHβ‰₯z) where z is a given number that satisfies e^z

  72. Probability

    Let X,Y,Z be three independent (i.e. mutually independent) random variables, each uniformly distributed on the interval [0,1]. 1. Find the mean and variance of 1/(Z+1). E[1/(Z+1)]= var(1/(Z+1))= 2. Find the mean of XY/(Z+1). Hint: Use your answer to the

  73. probability theory

    Let X, Y, Z, be independent discrete random variables. Let A= X(Y+Z) and B= XY With A, B, X, defined as before, determine wheter the folllowing statements are true or false. 1. A and B are independent 2. A and B are conditionally independent, given X = 0.

  74. math , probability

    Let X1, X2, ... be a sequence of independent random variables, uniformly distributed on [0,1]. Define Nn to be the smallest k such that X1 + X2 + ... + Xx exceeds cn = 5 + 12/n, namely, Nn = min{k >1: X1 + X2 +...+Xk > cn} Does the limit lim P (NK>n) 100

  75. Statistics

    A simple random sample of cars in a city was categorized according to fuel type and place of manufacture. domestic foreign gasoline 146 191 diesel 18 26 hybrid 51 79 Are place of manufacture and fuel type independent? If the two variables were independent,

  76. Probability

    Let X and Y be independent random variables, each uniformly distributed on the interval [0,2]. Find the mean and variance of XY. E[XY]= - unanswered var[XY]= - unanswered Find the probability that XYβ‰₯1. Enter a numerical answer. P(XYβ‰₯1)= - unanswered

  77. communication

    X and Y are discrete jointly distributed discrete valued random variables. The relation between their joint entropy H(X,Y) and their individual entropies H(X),H(Y) is H(X,Y)≀H(X)+H(Y), equality holds when X,Y are independent H(X,Y)≀H(X)+H(Y), equality

  78. Statistics

    As above, let Y1,…,Yn denote the i 'th number in the binary data set. Recall that Y1,…,Yn are assumed to be independent and identically distributed (i.i.d.) as some distribution Y . In the future, we will abbreviate this assumption with the notation

  79. math(Quantitative) ...Pls help me

    Linear regression analysis is based on identifying independent variables and gathering historical data for these variables.Name 2 independent variables to forecast these dependent variables: (a)Demand for hospital Services. (b)Students entering Legon

  80. Regression Analysis

    1)Quantity of Beef 2)Price of Beef 3)Price of Pizza 4)Price of Coke 5)Income 1- list and explain each of the components of your regression model, both the dependent variable and the independent variables 2-list each of the independent variables,

  81. math

    Let X and Y be two independent, exponentially distributed random variables with parameters ,lambda and mu, respectively. 1.Find P(X

  82. math221

    consider situations in your work or home that could be addressed through a continuous probability distribution. Describe the situation and the variables, and determine whether the variables are normally distributed or not. How could you change these to a

  83. science

    Writing variables and hypothesses What about them? i don't even understand them and i have to make up 4 variables and hypothesses about independent and dependent variables i don't even understand them and i have to make up 4 variables and hypothesses about

  84. Statistics

    Let U1,…,Un be i.i.d. random variables uniformly distributed in [0,1] and let Mn=max1≀i≀nUi . Find the cdf of Mn , which we denote by G(t) , for t∈[0,1] .

  85. math

    let two stochastically independent random variables y1 and y2 with the distribution b(n1,p1) and b(n2,p2) respectively,how find a confidence interval for p1-p2 ?

  86. statistics

    Let X be the average of a sample of 16 independent normal random variables with mean 0 and variance 1. Determine c such that P (X< c) = .5

  87. Maths

    Approximate the probability that the sum of the 16 independent uniform (0,1) random variables exceeds 10.

  88. Math

    Random variables X and Y are both normally distributed with mean 100 and standard deviation 4. It is known that random variable X+Y is also a normal distribution. a. What is the mean of X+Y? b. What is the standard deviation of X+Y? I see that the mean is

  89. Stats

    In each of the four examples listed below, one of the given variables is independent (x) and one of the given variables is dependent (y). Indicate in each case which variable is independent and which variable is dependent. I. Rainfall; Crop yield II. Taxi

  90. science

    what should you ask yourself when looking for an independent variable in an experiment? I would ask whether that variable can be manipulated or not. Here is more info on experimental variables that might be helpful. An independent variable is the potential

  91. Statisitcs

    Suppose that X and Y are independent discrete random variables and each assumes the values 0,1, and 2 with probability of 1/3 each. Find the frequency function of X+Y.

  92. Stats

    6. In each of the four examples listed below, one of the given variables is independent (x) and one of the given variables is dependent (y). Indicate in each case which variable is independent and which variable is dependent. I. Rainfall; Crop yield II.

  93. Experiment

    The question is how do I design a basic experiment that would allow us to establish a cause-effect relationship between number of hours worked per week and lower college graduation rates? It must have these components: a manupulated independent variable, a

  94. statistics

    The profit for a new product is given by Z = 2X - 2Y - 7. We know that X and Y are independent random variables with Var(X) = 2 and Var(Y) = 2.7. What is the variance of Z?

  95. math

    8 divided by 3 plus 6= You asked 8 divided by 3 plus 6= (8/3) + 6 = 2(2/3) + 6 or 8/3 + 18/3 = ??/3 I don't understand how to describe pairs of related variables what's the difference between dependent & independent variables I'm not what class your

  96. College Stats

    Suppose that two random variables X1 and X2 have a bivariate normal distribution, and Var(X1) = Var(X2). Show that the sum X1+X2 and the difference X1βˆ’ X2 are independent.

  97. Math Probability

    Let X and Y be independent random variables, each uniformly distributed on the interval [0,2]. Find the mean and variance of XY. E[XY]= var[XY]= Find the probability that XYβ‰₯1. Enter a numerical answer. P(XYβ‰₯1)=

  98. STATISTICS

    1. What if the size for each sample were increased to 20? Would a sample mean of 115 or more be considered unusual? Why or why not? 2. Why is the Central Limit Theorem used? 3. Consider situations in your work or home that could be addressed through a

  99. math

    let two stochastically independent random variables y1 and y2 with the distribution b(100,p1) and b(100,p2) respectively,y1=50 and y2=40 ,find 90% a confidence interval for p1-p2 ?

  100. science

    _____ are factors that are not tested and remain constant. A. Dependent variables B. Controlled variables C. Independent variables D. Constant variables

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