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We also provide a Why buy extra books when you can get all the homework help you need in one place? degroot manual pdf probability and statistics degroot And Statistics 4th Edition, Degroot Schervish Morris Herman DeGroot (June 8, 1931 – November 2, 1989) was an American Probability and Statistics, 4th Edition. Question : 1SE - Let A1, A2,... be an infinite sequence of events such that A1 ? A2 ? .... Prove that Pr ? i=1 Ai = limn?? Pr(An). Hint: Consider the sequence Ac 1, Ac 2,..., and apply Exercise 12. Question : 2SE - Suppose that a coin is tossed seven times. Let A denote the event that a head is obtained on the first toss, and let B denote the event that a head is obtained on the fifth toss. Are A and B disjoint? Question : 3SE - If A, B, and D are three events such that Pr(A ? B ? D) = 0.7, what is the value of Pr(Ac ? Bc ? Dc)? Question : 4SE - Suppose that a certain precinct contains 350 voters, of which 250 are Democrats and 100 are Republicans. If 30 voters are chosen at random from the precinct, what is the probability that exactly 18 Democrats will be selected? Question : 5SE - Suppose that in a deck of 20 cards, each card has one of the numbers 1, 2, 3, 4, or 5 and there are four cards with each number. If 10 cards are chosen from the deck at random, without replacement, what is the probability that each of the numbers 1, 2, 3, 4, and 5 will appear exactly twice? Question : 6SE - Consider the contractor in Example 1.5.4 on page 19. He wishes to compute the probability that the total utility demand is high, meaning that the sum of water and electrical demand (in the units of Example 1.4.5) is at least 215. Draw a picture of this event on a graph like Fig. 1.5 or Fig. 1.9 and find its probability. Question : 7SE - Suppose that a box contains r red balls and w white balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. (a) What is the probability that all r red balls will be obtained before any white balls are obtained? (b) What is the probability that all r red balls will be obtained before two white balls are obtained? Question : 8SE - Suppose that a box contains r red balls, w white balls, and b blue balls. Suppose also that balls are drawn from the box one at a time, at random, without replacement. What is the probability that all r red balls will be obtained before any white balls are obtained? Question : 9SE - Suppose that 10 cards, of which seven are red and three are green, are put at random into 10 envelopes, of which seven are red and three are green, so that each envelope contains one card. Determine the probability that exactly k envelopes will contain a card with a matching color (k = 0, 1,..., 10). Question : 10SE - Suppose that 10 cards, of which five are red and five are green, are put at random into 10 envelopes, of which seven are red and three are green, so that each envelope contains one card. Determine the probability that exactly k envelopes will contain a card with a matching color (k = 0, 1,..., 10). Question : 11SE - Suppose that the events A and B are disjoint. Under what conditions are Ac and Bc disjoint? Question : 12SE - Let A1, A2, and A3 be three arbitrary events. Show that the probability that exactly one of these three events will occur is Pr(A1) + Pr(A2) + Pr(A3) ? 2 Pr(A1 ? A2) ? 2 Pr(A1 ? A3) ? 2 Pr(A2 ? A3) + 3 Pr(A1 ? A2 ? A3). Question : 13SE - Let A1,...,An be n arbitrary events. Show that the probability that exactly one of these n events will occur is n i=1 Pr(Ai) ? 2 i