# Question: If X Y and Z are independent random variables having

If X, Y, and Z are independent random variables having identical density functions f(x) = e−x, 0 < x < ∞, derive the joint distribution of U = X + Y, V = X + Z, W = Y + Z.

## Relevant Questions

In Example 8b, let Show that Y1, . . . ,Yk, Yk+1 are exchangeable. Yk+1 is the number of balls one must observe to obtain a special ball if one considers the balls in their reverse order of withdrawal. Show that the jointly continuous (discrete) random variables X1, . . . ,Xn are independent if and only if their joint probability density (mass) function f (x1, . . . , xn) can be written as for nonnegative functions gi(x), ...Let X1, X2, X3 be independent and identically distributed continuous random variables. Compute (a) P{X1 > X2|X1 > X3}; (b) P{X1 > X2|X1 < X3}; (c) P{X1 > X2|X2 > X3}; (d) P{X1 > X2|X2 < X3}. Show that if n people are distributed at random along a road L miles long, then the probability that no 2 people are less than a distance D miles apart is when D ≤ L/(n − 1), [1 − (n − 1)D/L]n. What if D > L/(n − ...(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 ...Post your question