# Question

(a) If X has a gamma distribution with parameters (t, λ), what is the distribution of cX, c > 0?

(b) Show that

has a gamma distribution with parameters n, λ when n is a positive integer and χ22n is a chi-squared random variable with 2n degrees of freedom.

(b) Show that

has a gamma distribution with parameters n, λ when n is a positive integer and χ22n is a chi-squared random variable with 2n degrees of freedom.

## Answer to relevant Questions

Let X and Y be independent continuous random variables with respective hazard rate functions λX(t) and λY(t), and set W = min(X,Y). (a) Determine the distribution function of W in terms of those of X and Y. (b) Show that ...The positive random variable X is said to be a lognormal random variable with parameters μ and σ2 if log(X) is a normal random variable with mean μ and variance σ2. Use the normal moment generating function to find the ...Show that X is stochastically larger than Y if and only if E[f(X)] ≥ E[f(Y)] for all increasing functions f . Show that X ≥st Y, then E[f(X)] ≥ E[f(Y)] by showing that f(X) ≥st f(Y) and then using Theoretical ...The game of Clue involves 6 suspects, 6 weapons, and 9 rooms. One of each is randomly chosen and the object of the game is to guess the chosen three. There are 4 different types of coupons, the first 2 of which compose one group and the second 2 another group. Each new coupon obtained is type I with probability pi, where p1 = p2 = 1/8, p3 = p4 = 3/8. Find the expected ...Post your question

0