# Question: In Problem 70 suppose that the coin is tossed n

In Problem 70, suppose that the coin is tossed n times. Let X denote the number of heads that occur. Show that

P{X = i} = 1/n + 1 i = 0, 1, . . . , n

Make use of the fact that

when a and b are positive integers.

Problem 70

Consider an urn containing a large number of coins, and suppose that each of the coins has some probability p of turning up heads when it is flipped. However, this value of p varies from coin to coin. Suppose that the composition of the urn is such that if a coin is selected at random from it, then the p-value of the coin can be regarded as being the value of a random variable that is uniformly distributed over [0, 1]. If a coin is selected at random from the urn and flipped twice, compute the probability that

(a) The first flip results in a head;

(b) Both flips result in heads.

P{X = i} = 1/n + 1 i = 0, 1, . . . , n

Make use of the fact that

when a and b are positive integers.

Problem 70

Consider an urn containing a large number of coins, and suppose that each of the coins has some probability p of turning up heads when it is flipped. However, this value of p varies from coin to coin. Suppose that the composition of the urn is such that if a coin is selected at random from it, then the p-value of the coin can be regarded as being the value of a random variable that is uniformly distributed over [0, 1]. If a coin is selected at random from the urn and flipped twice, compute the probability that

(a) The first flip results in a head;

(b) Both flips result in heads.

**View Solution:**## Answer to relevant Questions

Suppose that in Problem 70 we continue to flip the coin until a head appears. Let N denote the number of flips needed. Find (a) P{N ≥ i}, i ≥ 0; (b) P{N = i}; (c) E[N]. Problem 70 Consider an urn containing a large ...N people arrive separately to a professional dinner. Upon arrival, each person looks to see if he or she has any friends among those present. That person then sits either at the table of a friend or at an unoccupied table if ...Suppose that X1 and X2 are independent random variables having a common mean μ. Suppose also that Var(X1) = σ21 and Var(X2) = σ22. The value of μ is unknown, and it is proposed that μ be estimated by a weighted average ...Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X] = 1.8, what is (a) The largest possible value of P{X = 3}? (b) The smallest possible value ...Let X be a normal random variable with parameters μ = 0 and σ2 = 1, and let I, independent of X, be such that P{I = 1} = 1/2 = P{I = 0}. Now define Y by In words, Y is equally likely to equal either X or −X. (a) Are X ...Post your question