# Question

Consider an urn containing n balls numbered 1, . . . , n, and suppose that k of them are randomly withdrawn. Let Xi equal 1 if ball number i is removed and let Xi be 0 otherwise. Show that X1, . . . ,Xn are exchangeable.

## Answer to relevant Questions

The joint probability density function of X and Y is given by f (x, y) = 6/7(x2 + xy/2) 0 < x < 1, 0 < y < 2 (a) Compute the density function of X. (b) Find P{X > Y}. (c) Find P{Y > 1/2|X < 1/2}. Suppose that X and Y are independent geometric random variables with the same parameter p. Without any computations, what do you think is the value of P{X = i|X + Y = n}? Imagine that you continually flip a coin having ...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. Verify Equation (6.6), which gives the joint density of X(i) and X(j). Let X1, . . . ,Xn be independent exponential random variables having a common parameter λ. Determine the distribution of min(X1, . . . ,Xn).Post your question

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