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Consider an experiment of tossing two coins three times. Coin A is fair but coin B...

Consider an experiment of tossing two coins three times. Coin A is fair but coin B is not with P(H)= 1/4 and P(T)= 3/4. Consider a bivariate random variable (X,Y) where X denotes the number of heads resulting from coin A and Y denotes the number of heads resulting from coin B.

(a) Find the range of (X,Y)

(b) Find the joint probability mass function of (X,Y).

(c) Find P(X=Y), P(X>Y), P(X+Y<=4).

(d) Find the marginal distributions of X and Y.

(e) Are X and Y independent?

(f) Determine the Covariance of X and Y.

Math   Statistics-And-Probability   
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