# Question: If the probability is 0 20 that a certain bank will

If the probability is 0.20 that a certain bank will refuse a loan application, use the normal approximation to determine (to three decimals) the probability that the bank will refuse at most 40 of 225 loan applications.

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Perform a suitable change of variable to show that the integral defining the gamma function can be written as If X has a binomial distribution with n = 3 and θ = 1/3 , find the probability distributions of (a) Y = X / 1+ X ; (b) U = (X – 1)4. If X has a uniform density with α = 0 and β = 1, show that the random variable Y = –2 ∙ lnX has a gamma distribution. What are its parameters? If X1, X2, and X3 have the multinomial distribution (see Definition 5.8 on page 165) with n = 2, θ1 = 14 , θ2 = 13 , and θ3 = 5/12 , find the joint probability distribution of Y1 = X1 + X2, Y2 = X1 – X2, and Y3 = X3. Rework Exercise 7.34 by using Theorem 7.2 to determine the joint probability density of U = Y – X and V = X and then finding the marginal density of U.Post your question