1. Suppose you have two random variables, X and Y with joint distribution given by the following table: X=0 X=1 Y=0 .4 .

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1. Suppose you have two random variables, X and Y with joint
distribution given by the following table: X=0 X=1 Y=0 .4 .2 Y=1 .1
.3 So, for example, the probability that Y = 0, X = 0 is .4, and
the probability that Y = 0 = .4 + .2 = .6. (a) Find the marginal
distributions (pmfs) of X and Y , denoted f(X), f(Y ). (b) Find the
conditional distribution (pmf) of Y give X, denoted f(Y |X). (c)
Find the expected values of X and Y , E(X), E(Y ). (d) Find the
variances of X and Y , V ar(X), V ar(Y ). (e) Find the covariance
of X and Y , Cov(X, Y ). (f) Find the correlation of X and Y , ρ(X,
Y ). (g) Are X and Y independent? Why or why not?