Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15...
Problem 3 (10 points). What are the expected value and variance of the number of full house hands in 100 poker hands? A poker hand consists of five randomly selected cards from an ordinary deck of 52 cards. It is a full house if three cards are of one denomination and two cards are of another denomination: for example, three queens and two 4's Problem 4 (10 points). Let X be a binomial random variable with parameters n 15 and...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
Problem 5. Let X be a binomial random variable with parameters n and p. Suppose that we want to generate a random variable Y whose probability mass function is the same as the conditional mass function of X given X-k, for some k-n. Let a = P(X-k), and suppose that the value of a has been computed (a) Give the inverse transform method for generating Y. (b) Give a second method for generating Y (c) For what values of a,...
Let X be a random variable, which has a binomial distribution with parameters n and p. It is known that E(X) = 12 and Var(X) = 4. Find n and p.
Problem 1. (a) Let X be a Binomial random variable such that E(X) 4 and Var(x) 2. Find the parameters of X (b) Let X be a standard normal random variable. Write down one function f(t) so that the random variable Y-f(X) is normal with mean a and variance b.
Let X be a binomial random variable with n = 5 and p = 0.30 Use the Binomial Tables to obtain the correct probability distribution Find each probability. 1) P(X = 5) 2) P(X ?= 1)
Let X be random variable with the binomial distribution with parameters n and 0 < p < 1. (1) Show that (P(X = x) / P(X = x -1)) - 1 = np + (p - x)) / (x(1-p)) for any 1 ≤ x ≤ n. (2) Show that when 0 ≤ x < (n + 1)p , P(X = x) is an increasing function x and for (n + 1)p < x ≤ n, P(X = x) is a...
Let N be a binomial random variable with p = 0.2 and n = 10. We roll a fair die N times, let X be the number of times we roll the number 1. Find the joint probability mass function of N and X.
Let X be a binomial random variable with n = 6, p = 0.4. Find the following values. (Round your answers to three decimal places.) (a) PCX = 4) (b) PIX S1 (c) PCX > 1) (d) 4 = 0 = o v npg Need Help? Read It 5. (-/6 Points) DETAILS MENDSTATC4 5.1.011 Let X be a binomial random variable with n = 10 and p = 0.3. Find the following values. (Round your answers to three decimal places.)...
Let X be a binomial random variable with n = 15 and p = 0.6. Calculate the following two probabilities, using an appropriate approximation method: • P(X = 4) • P(7 ≤ X < 10)