# Question

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 ith ball selected is white, and let it equal 0 otherwise. Give the joint probability mass function of

(a) X1, X2;

(b) X1, X2, X3.

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 ith ball selected is white, and let it equal 0 otherwise. Give the joint probability mass function of

(a) X1, X2;

(b) X1, X2, X3.

## Answer to relevant Questions

The joint density function of X and Y is given by f (x, y) = xe−x(y+1) x > 0, y > 0 (a) Find the conditional density of X, given Y = y, and that of Y, given X = x. (b) Find the density function of Z = XY. 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 and Y are independent and identically distributed uniform random variables on (0, 1), compute the joint density of U = X + Y, V = X/Y 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 U denote a random variable uniformly distributed over (0, 1). Compute the conditional distribution of U given that (a) U > a; (b) U < a; where 0 < a < 1.Post your question

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