# Question: Let X1 and X2 be two independent random variables Let

Let 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?

(a) Find the mgf of X2.

(b) What is its distribution?

## Relevant Questions

Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means μ1, μ2, . . . , μn is Poisson with mean μ1 + μ2 + · · · + μn. Let T have a t distribution with r degrees of freedom. Show that E(T) = 0 provided that r ≥ 2, and Var(T) = r/(r − 2) provided that r ≥ 3, by first finding E(Z), E(1/√U), E(Z2), and E(1/U). At certain times during the year, a bus company runs a special van holding 10 passengers from Iowa City to Chicago. After the opening of sales of the tickets, the time (in minutes) between sales of tickets for the trip has a ...A die is rolled 24 independent times. Let Y be the sum of the 24 resulting values. 0Recalling that Y is a random variable of the discrete type, approximate (a) P(Y ≥ 86). (b) P(Y < 86). (c) P(70 < Y ≤ 86). Let be the mean of a random sample of size n = 15 from a distribution with mean μ = 80 and variance σ2 = 60. Use Chebyshev’s inequality to find a lower bound for P(75 < < 85).Post your question