Question

Can someone please answer these 3 by Friday?

Problem 2 Let D, E, F, G, and H be events such that P(D) = 0.7, P(E) = 0.6, P(F) = 0.8, P(G) = 0.9, and P(H) = 0.5. Suppose that Dc, E, Fc, Gc, and H are independent.
(a) Find the probability that all of the events D, E, F, G, and H occur.
(b) Find the probability that at least one of the events D, E, F, G, and H occurs.

Problem 3 Five men and five women are ranked according to their scores on an examination. Assume that no two scores are alike, and all 10! possible rankings are equally likely. Let X denote the highest ranking achieved by a woman (for example, X = 2 if the top-ranked person was a man, and the next-ranked person was a woman). Find the probability mass function (pmf) of the random variable X, and plot the cumulative distribution function (cdf) of X.

Problem 4 Suppose there are three cards numbered 2, 7, 10, respectively. Suppose you are to be offered these cards in random order. When you are offered a card, you must immediately either accept it or reject it. If you accept a card, the process ends. If you reject a card, then the next card (if there is one) is offered. If you reject the first two cards, you have to accept the final card. You plan to reject the first card offered, and then to accept the next card if and only if its value is greater than the value of the first card. Let X be a number on the card you have accepted in the end. Find the pmf of X and plot the cdf of X.

Answer 1