1-The joint p.m.f of two random variables X, Y are are given by

P(X=x,Y=y)=1/3 for (x,y) =(-1,0), (0,1), (1,0)

0otherwise

1a. Find Cov(X,Y)

1b. Are the random variables independent? Why, why not?

2-Let X ~ Normal(a,b2). Define new random variable W=[(X-a)/b ]2

2a. Find the pdf of W

2b. Compute E(W2)

4-Two species are competing in a region for control of a limited amount of a certain resource.

The random variable X denote the proportion of the resource controlled by species 1 and supposeXUniform(0,1)

. Define a new random variable Y denoting the proportion of the resource controlled by the dominant species. Find P(Y<0.25)

4-a 0

4-b 0.5

4-c 1