# Question: Choose a number X at random from the set of

Choose a number X at random from the set of numbers {1, 2, 3, 4, 5}. Now choose a number at random from the subset no larger than X, that is, from {1, . . . ,X}. Call this second number Y.

(a) Find the joint mass function of X and Y.

(b) Find the conditional mass function of X given that Y = i. Do it for i = 1, 2, 3, 4, 5.

(c) Are X and Y independent? Why?

(a) Find the joint mass function of X and Y.

(b) Find the conditional mass function of X given that Y = i. Do it for i = 1, 2, 3, 4, 5.

(c) Are X and Y independent? Why?

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

Repeat Problem 2 when the ball selected is replaced in the urn before the next selection. Problem 2 Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white and 8 red balls. Let Xi equal 1 if the ...A complex machine is able to operate effectively as long as at least 3 of its 5 motors are functioning. If each motor independently functions for a random amount of time with density function f (x) = xe−x, x > 0, compute ...X and Y have joint density function f(x, y) = 1/x2y2 x ≥ 1, y ≥ 1 (a) Compute the joint density function of U = XY, V = X/Y. (b) What are the marginal densities? The lifetimes of batteries are independent exponential random variables, each having parameter λ. A flashlight needs 2 batteries to work. If one has a flashlight and a stockpile of n batteries, what is the distribution of ...Suppose that the number of events occurring in a given time period is a Poisson random variable with parameter λ. If each event is classified as a type i event with probability pi, i = 1, . . . , n, ∑ pi = 1, ...Post your question