# Question: The joint density of X and Y is given by a

The joint density of X and Y is given by

(a) Are X and Y independent? If, instead, f (x, y) were given by

(b) Would X and Y be independent?

(a) Are X and Y independent? If, instead, f (x, y) were given by

(b) Would X and Y be independent?

## Relevant Questions

Let f (x, y) = 24xy 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ x + y ≤ 1 and let it equal 0 otherwise. (a) Show that f (x, y) is a joint probability density function. (b) Find E[X]. (c) Find E[Y]. If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find the distribution of Z = X1/X2. Also compute P{X1 < X2}. The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be (a) More than 2 such accidents in the next month? (b) More than 4 such accidents in the next ...If X1, X2, X3 are independent random variables that are uniformly distributed over (0, 1), compute the probability that the largest of the three is greater than the sum of the other two. 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/YPost your question