Question

find marginal and conditional densities of x,y Are X,Y independent also compute p(x<=1 ,y<=1)​

Answer 1

Problem 1 : The joint probability distribution of two random variables X and Y is given in the following table

Y

X 0 1 2 3

f(x)

2 1/12 1/12 1/12 1/12

3 1/12 1/6 1/12 0

4 1/12 1/12 0 1/6

f(y)

a) Find the marginal density of X and the marginal density of Y. (add them to the above table)

b) Are X and Y independent?

c) Compute the P{Y>1| X>2}

d) Compute the expected value of X.

e) Compute the probability that X is greater or equal to Y+1.

f) Compute the conditional probability distribution of X given Y=3.