# Question: The joint density function of X and Y is a Are

The joint density function of X and Y is

(a) Are X and Y independent?

(b) Find the density function of X.

(c) Find P{X + Y < 1}.

(a) Are X and Y independent?

(b) Find the density function of X.

(c) Find P{X + Y < 1}.

## Answer to relevant Questions

The random variables X and Y have joint density function f (x, y) = 12xy(1 − x) 0 < x < 1, 0 < y < 1 and equal to 0 otherwise. (a) Are X and Y independent? (b) Find E[X]. (c) Find E[Y]. (d) Find Var(X). (e) Find Var(Y). The gross weekly sales at a certain restaurant is a normal random variable with mean $2200 and standard deviation $230. What is the probability that (a) The total gross sales over the next 2 weeks exceeds $5000; (b) Weekly ...In Problem 5, calculate the conditional probability mass function of Y1 given that (a) Y2 = 1; (b) Y2 = 0. Problem 5 Repeat Problem 3a when the ball selected is replaced in the urn before the next selection. Problem 3 In ...If X1, X2, X3, X4, X5 are independent and identically distributed exponential random variables with the parameter λ, compute (a) P{min(X1, . . . ,X5) ≤ a}; (b) P{max(X1, . . . ,X5) ≤ a}. 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.Post your question