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NOTE:KINDLY SOLVE PARTS D AND E. A fair coin is tossed four times, and the random...

NOTE:KINDLY SOLVE PARTS D AND E.

A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Y is the number of heads in the last three tosses.
a) What is the joint probability mass function of X and Y ?
b) What are the marginal probability mass functions of X and Y ?
c) Are the random variables X and Y independent?
d) What are the expectations and variances of the random variables X and Y ?
e) If there is one head in the last three tosses, what is the conditional probability mass function of X? What are the conditional expectation and variance of X?

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Here you asked d and e only. That's why I done d) and e).

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