# Question

Derive the distribution of the range of a sample of size 2 from a distribution having density function

f(x) = 2x, 0 < x < 1.

f(x) = 2x, 0 < x < 1.

## Answer to relevant Questions

Let X and Y denote the coordinates of a point uniformly chosen in the circle of radius 1 centered at the origin. That is, their joint density is f(x, y) = 1/π x2 + y2 ≤ 1 Find the joint density function of the polar ...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. In Example 5c we computed the conditional density of a success probability for a sequence of trials when the first n + m trials resulted in n successes. Would the conditional density change if we specified which n of these ...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. Suggest a procedure for using Buffon’s needle problem to estimate π. Surprisingly enough, this was once a common method of evaluating π.Post your question

0