3 A fair coin is tossed three times and the random variable

3. A fair coin is tossed three times, and the random variable X is the number of heads in the first two tosses and the random variable Y is the number of heads in the last two tosses.

a) What is the joint and marginal probability mass function of X and Y?                   

b) What is the probability that both X and Y have the same number of tails?      

c) What is the conditional probability of X given Y has two heads?

d) Are X and Y independent of each other? Why or why not?      

e) What is the covariance of X and Y?   

f) What is the correlation of X and Y? Discuss the result.

Solution