# Question: If X and Y are independent and identically distributed uniform

If X and Y are independent and identically distributed uniform random variables on (0, 1), compute the joint density of

U = X + Y, V = X/Y

U = X + Y, V = X/Y

**View Solution:**## Answer to relevant Questions

If X1 and X2 are independent exponential random variables, each having parameter λ, find the joint density function of Y1 = X1 + X2 and Y2 = eX1. Verify Equation (1.2). Suppose that Xi, i = 1, 2, 3 are independent Poisson random variables with respective means λi, i = 1, 2, 3. Let X = X1 + X2 and Y = X2 + X3. The random vector X, Y is said to have a bivariate Poisson distribution. Find its ...If X is exponential with rate λ, find P{[X] = n,X − [X] ≤ x}, where [x] is defined as the largest integer less than or equal to x. Can you conclude that [X] and X − [X] are independent? If X and Y are independent continuous positive random variables, express the density function of (a) Z = X/Y and (b) Z = XY in terms of the density functions of X and Y. Evaluate the density functions in the special case ...Post your question