# Question: Let X and Y be two independent random variables having

Let X and Y be two independent random variables having identical gamma distributions.

(a) Find the joint probability density of the random variables U = X / X + Y and V = X + Y.

(b) Find and identify the marginal density of U.

(a) Find the joint probability density of the random variables U = X / X + Y and V = X + Y.

(b) Find and identify the marginal density of U.

## Answer to relevant Questions

On page 215 we indicated that the method of transformation based on Theorem 7.1 can be generalized so that it applies also to random variables that are functions of two or more random variables. So far we have used this ...If n independent random variables have the same gamma distribution with the parameters α and β, find the moment-generating function of their sum and, if possible, identify its distribution. If X1 and X2 are independent random variables having exponential densities with the parameters θ1 and θ2, use the distribution function technique to find the probability density of Y = X1 + X2 when (a) θ1 ≠ θ2; (b) ...Describe how the probability integral transformation might have been used by the writers of the software that you used to produce the result of Exercise 7.56. If X is the number of 7’s obtained when rolling a pair of dice three times, find the probability that Y = X2 will exceed 2.Post your question