# probability

The random variables X and Y have the joint PMF

pX,Y(x,y)={c⋅(x+y)2,0,if x∈{1,2,4} and y∈{1,3},otherwise.
All answers in this problem should be numerical.

Find the value of the constant c.

c=
Find P(Y<X).

P(Y<X)=
Find P(Y=X).

P(Y=X)=
Find the following probabilities.

P(X=1)=
P(X=2)=
P(X=3)=
P(X=4)=
Find the expectations E[X] and E[XY].

E[X]=
E[XY]=
Find the variance of X.

var(X)=

1. 👍
2. 👎
3. 👁
1. c= 5/64

P(Y<X)= 83/128

P(Y=X)= 1/32

P(X=1)= 10/64

P(X=2)= 17/64

P(X=3)= 0

P(X=4)= 37/64

E[X]= 3

E[XY]= 227/32

var(X)= 3/2

1. 👍
2. 👎

1. 👍
2. 👎
3. c=1/128

1. 👍
2. 👎

## Similar Questions

1. ### Probability

The random variables X and Y have a joint PDF of the form fX,Y(x,y)=c⋅exp{−12(4x2−8x+y2−6y+13)} E[X]= var(X)= E[Y]= var(Y)=

2. ### 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

3. ### Statistics

Z1,Z2,…,Zn,… is a sequence of random variables that converge in distribution to another random variable Z ; Y1,Y2,…,Yn,… is a sequence of random variables each of which takes value in the interval (0,1) , and which

4. ### 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

1. ### Probability

Let X and Y be two normal random variables, with means 0 and 3 , respectively, and variances 1 and 16 , respectively. Find the following, using the standard normal table. Express your answers to an accuracy of 3 decimal places. 1.

2. ### probability

The random variables X and Y have the joint PMF pX,Y(x,y)={c⋅(x+y)2,0,if x∈{1,2,4} and y∈{1,3},otherwise. All answers in this problem should be numerical. Find the value of the constant c. c=

3. ### 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

4. ### Math

1. The random variables X and Y are distributed according to the joint PDF fX,Y(x,y) = {ax2,0,if 1≤x≤2 and 0≤y≤x,otherwise. Find the constant a. 2. Determine the marginal PDF fY(y) . (Your answer can be either numerical or

1. ### Science Plzz Help

1. Which of the following types of joints allows the type of shoulder motion needed by a baseball pitcher to pitch a fastball in a baseball game? A. pivot B. gliding C. hinge D. ball and socket*** 2. Which of the following pairs

2. ### 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

3. ### probability

The random variables X and Y are jointly continuous, with a joint PDF of the form fX,Y(x,y)={cxy,if 0≤x≤y≤1 0,,otherwise, where c is a normalizing constant. For x∈[0,0.5], the conditional PDF fX|Y(x|0.5) is of the form

4. ### Math

For the discrete random variable X, the probability distribution is given by P(X=x)= kx x=1,2,3,4,5 =k(10-x) x=6,7,8,9 Find the value of the constant k E(X) I am lost , it is the bonus question in my homework on random variables