Solve these examples please.

Problem 1: Two cards are drawn without replacement from a pack of cards, and the random variable X' measures the number of hearts drawn and the random variable Y measures the number of clubs drawn 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 no hearts are drawn, what is the conditional probability mass function of Y ? If one heart is drawn, what is the conditional probability mass function of Y ? Problem 2; Repeat problem 1, if the second card is drawn with replacement Problem 3: 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 ? 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