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
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statistics
Let π and π be independent positive random variables. Let π=π/π. In what follows, all occurrences of π₯, π¦, π§ are assumed to be positive numbers. 1. Suppose that π and π are discrete, with known PMFs, ππ and ππ.

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

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, pZY(zy)=pX(?). What is the

probability
Let π and π be independent positive random variables. Let π=π/π . In what follows, all occurrences of π₯ , π¦ , π§ are assumed to be positive numbers. 1. Suppose that π and π are discrete, with known PMFs, ππ and ππ .

probability
For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,β¦ be independent continuous random variables, each uniformly distributed between β1 and 1. Let Ui=X1+X2+β―+Xii,i=1,2,β¦. What value does the

math
Conditioned on the result of an unbiased coin flip, the random variables T1,T2,β¦,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

Math
Searches related to The random variables X1,X2,β¦,Xn are continuous, independent, and distributed according to the Erlang PDF fX(x)=Ξ»3x2eβΞ»x2, for xβ₯0, where Ξ» is an unknown parameter. Find the maximum likelihood estimate of Ξ» , based on observed

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

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

probability and statistics
Let Ξ1, Ξ2, W1, and W2 be independent standard normal random variables. We obtain two observations, X1=Ξ1+W1,X2=Ξ1+Ξ2+W2. Find the MAP estimate ΞΈ^=(ΞΈ^1,ΞΈ^2) of (Ξ1,Ξ2) if we observe that X1=1, X2=3. (You will have to solve a system of two linear

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 β999". 1) Let X1, X2,β¦ be independent continuous

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, pZY(zy)=pX(?). What is the argument

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

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

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.

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

Probability
For each of the following sequences, determine the value to which it converges in probability. (a) Let X1,X2,β¦ be independent continuous random variables, each uniformly distributed between β1 and 1. Let Ui=X1+X2+β―+Xii,i=1,2,β¦. What value does the

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

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

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

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

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

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

Probability
1. Suppose three random variables X , Y , Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZβ£X(zβ£x)PYβ£Z(yβ£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

probability
Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let π and π be independent continuous random variables that are uniformly distributed on (0,1) . Let π»=(π+2)π . Find the probability π(lnπ»β₯π§) where

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

Probability
1.Let π and π be two binomial random variables: a.If π and π are independent, then π+π is also a binomial random variable b.If π and π have the same parameters, π and π , then π+π is a binomial random variable c.If π

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.

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 0β€zβ€1 : find fZ(z)

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

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 welldefined and finite. Let X and Y be two

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.

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 .

Probability
Suppose that we have a box that contains two coins: A fair coin: P(H)=P(T)=0.5 . A twoheaded 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

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.

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

Probability
Suppose that we have a box that contains two coins: A fair coin: P(H)=P(T)=0.5 . A twoheaded 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

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 =X1βX3, Y2 =X2βX3. We further introduce indicator random variables Ziβ{0,1} with Zi=1 if and only if Yi=0 for i=1,2 . Calculate

Math
Let π and π be independently random variables, with π uniformly distributed on [0,1] and π uniformly distributed on [0,2] . Find the PDF ππ(π§) of π=max{π,π} . For π§2 : ππ(π§)= For 0β€π§β€1 : ππ(π§)= For

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

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

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 =X1βX3, Y2 =X2βX3. We further introduce indicator random variables Ziβ{0,1} with Zi=1 if and only if Yi=0 for i=1,2 . 1. Calculate

Probability
Let N,X1,Y1,X2,Y2,β¦ 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

math
Let X1,X2,β¦ 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+n12ββββ , namely, Nn = min{kβ₯1:X1+X2+β―+Xk>cn} Does the limit limnββP(Nn>n)

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

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

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

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 0β€zβ€1 : 3. For 1β€zβ€2 :

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.

Probability
Let N,X1,Y1,X2,Y2,β¦ 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

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

probability
Let π and π be independent continuous random variables that are uniformly distributed on (0,1) . Let π»=(π+2)π . Find the probability π(lnπ»β₯π§) where π§ is a given number that satisfies π^π§

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

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)= ???

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

math, probability
Let X1,X2,β¦ 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+n12ββββ , namely, Nn = min{kβ₯1:X1+X2+β―+Xk>cn} Does the limit limnββP(Nn>n)

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

math , probability
Let π and π be independent random variables, uniformly distributed on [0,1]. Let π=min{π,π} and π=max{π,π}. Let π=π[ππ] and π=π[π]. 1. Find π. 2. Find π. 3. Find Cov(π,π). You can give either a

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 0β€zβ€1 : fZ(z)= For 1β€zβ€2 : fZ(z)=

probability
If two random variables π and π are independent, which conclusion in the following is not true

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

Probability
Let π΄ and π΅ be independent random variables with means 1, and variances 1 and 2, respectively. Let π=π΄βπ΅ and π=π΄+π΅. Find the coefficients π1 and π2 of the Linear Least Mean Squares (LLMS) estimator

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

probability
Let N,X1,Y1,X2,Y2,β¦ 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

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.

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,

Probability
Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter pβ(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

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

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

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

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

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

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.

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

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,

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

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)β€H(X)+H(Y), equality holds when X,Y are independent H(X,Y)β€H(X)+H(Y), equality

Statistics
As above, let Y1,β¦,Yn denote the i 'th number in the binary data set. Recall that Y1,β¦,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

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

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 2list each of the independent variables,

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

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

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

Statistics
Let U1,β¦,Un be i.i.d. random variables uniformly distributed in [0,1] and let Mn=max1β€iβ€nUi . Find the cdf of Mn , which we denote by G(t) , for tβ[0,1] .

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 p1p2 ?

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

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

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

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

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

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.

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.

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

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?

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

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 X1β X2 are independent.

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)=

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

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 p1p2 ?

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