Let M have a binomial distribution with parameters N and p. Conditioned on M, the random...
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 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 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...
(2) Let Y be a binomial random variable with parameters n and p. Remember that We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n借)(1-n) (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator
A random variable X has binomial distribution with parameters n = 11 and theta = 0.28. P(X > 2) = ________________
(2) Let Y be a binomial random variable with parameters n and p. Remember that E(Y) V(Y)p1 -p) We know that Y/n is an unbiased estimator of p. Now we want to estimate the variance of Y with n(2(1 (a) Find the expected value of this estimator (b) Find an unbiased estimator that is a simple modification of the proposed estimator
Suppose that X is a random variable from a binomial distribution with parameters n=12 and p. Consider the point estimate p̂=X/14 1. what's the bias of this estimate? 2. what is the value of the mean square error of this estimate if the actual value of p is 0.735
Let x be a random variable from a binomial distribution with n = 40 and p = 0.9. If a normal approximation is appropriate, give the distribution of x' that would be used in the approximation. a) x' ~ N(40, 0.92) b) x' ~ N(36, 3.62) c) x' ~ N(36, 1.92) d) normal approximation is not appropriate
From textbook: "Let X have a negative binomial distribution with parameters r and p such that: Find E[X] and Var[X] without using the definition; instead, consider how X can be written as a sum of independent random variables." Question: How do I do this? p(k) = p' (1-p)*-, k=r,r+1,..