Question: The time X in minutes of a visit to a
The time X in minutes of a visit to a cardiovascular disease specialist by a patient is modeled by a gamma pdf with α = 1.5 and θ = 10. Suppose that you are such a patient and have four patients ahead of you. Assuming independence, what integral gives the probability that you will wait more than 90 minutes?
Answer to relevant QuestionsLet X1 and X2 be two independent random variables. Let X1 and Y = X1 + X2 be χ2(r1) and χ2(r), respectively, where r1 < r. (a) Find the mgf of X2. (b) What is its distribution? Let the independent random variables X1 and X2 be N(0,1) and χ2(r), respectively. Let Y1 = X1/√X2/r and Y2 = X2. (a) Find the joint pdf of Y1 and Y2. (b) Determine the marginal pdf of Y1 and show that Y1 has a t ...Let X and Y equal the respective numbers of hours a randomly selected child watches movies or cartoons on TV during a certain month. From experience, it is known that E(X) = 30, E(Y) = 50, Var(X) = 52, Var(Y) = 64, and ...If X is b(100,0.1), find the approximate value of P(12 ≤ X ≤ 14), using (a) The normal approximation. (b) The Poisson approximation. (c) The binomial. If the distribution of Y is b(n, 0.5), give a lower bound for P(|Y/n − 0.5| < 0.08) when (a) n = 100. (b) n = 500. (c) n = 1000.
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