Suppose a fair coin is tossed 3 times and let a random variable X denote the number of heads. Define Y, a Bernoulli random variable, as Y=1 if the first tossed coin turns up head, and Y=0 otherwise.
(i) Determine and sketch the pdf of X and cdf of X.
(ii) Determine the joint probability density function of (X, Y)
(iii) Are random variables X and Y independent? Explain.
(iv) Compute P(X=2|Y=1), Cov(X,Y) and Corr(X, Y)