Question: In the casino game roulette the probability of winning with
In the casino game roulette, the probability of winning with a bet on red is p = 18/38. Let Y equal the number of winning bets out of 1000 independent bets that are placed. Find P(Y > 500), approximately.
Answer to relevant QuestionsIf X is b(100,0.1), find the approximate value of P(12 ≤ X ≤ 14), using (a) The normal approximation. (b) The Poisson approximation. (c) The binomial. Let X equal the number out of n = 48 mature aster seeds that will germinate when p = 0.75 is the probability that a particular seed germinates. Approximate P(35 ≤ X ≤ 40). Let Y be χ2(n). Use the central limit theorem to demonstrate that W = (Y − n)/√2n has a limiting cdf that is N(0, 1). In the casino game roulette, if a player bets $1 on red (or on black or on odd or on even), the probability of winning $1 is 18/38 and the probability of losing $1 is 20/38. Suppose that a player begins with $5 and makes ...Let X1, X2, . . . , Xn be a random sample from b(1, p) (i.e., n Bernoulli trials). Thus, (a) Show that = Y/n is an unbiased estimator of p. (b) Show that Var(X) = p(1 − p)/n. (c) Show that E[(1 − X)/n] = (n − 1)[p(1 ...
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