Letxbe the maximum of the number of heads obtained when carlos and michael each flipa fair coin twice.(a) describe the underlying spacesof this random experiment and specify the probabil-ities of its elementary events.(b) show the mapping fromstosx, the range ofx.(c) find the probabilities for the various values ofx.(d) compare the pmf ofxwith the pmf ofy, the number of heads in two tosses of a faircoin. explain the difference.(e) suppose that carlos uses a coin with probability of headsp= 3/4. find the pmf ofx.(f) back to the assumption that coins are fair, find the conditional pmf ofx, the maximumof coin tosses, given thatx > 0.(g) find the probability pmf ofxgiven that michael got one head in two tosses.(h) find the probability pmf ofxgiven that michael got one head in the first toss.(i) now make the assumption in part (e) again and find the probability that carlos gotthe maximum given thatx= 2.