STAT 5100 Midterm: STAT 5100 Iowa Midterm1
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Please write your answers in the exam books provided. You can use formulas from page 2 when appropriate: (5 points) a continuous random variable x has probability density function f (x) =(c/x3. Given this information, nd the conditional probability that the rst ve ips result in three heads and two tails: (5 points) let x have a uniform distribution on [0, 1] and let. Find the density of y : (5 points) an experiment is conducted with the following steps, a fair die is rolled, resulting in a number k {1, . Find the probability that the value produced by the experiment is 3. P (x = x|p) = px(1 p)1 x; x = 0, 1; 0 p 1. Bernoulli(p) pmf mean, variance e[x] = p, var(x) = p(1 p) mgf. Binomial(n, p) pmf mean, variance e[x] = np, var(x) = np(1 p) mgf. Poisson( ) pmf mean, variance e[x] = , var(x) = mgf.
