Suppose the random variable X has the cdf F(x) = 0, x < −1, = (x+2)/4, −1 ≤ x < 1, = 1, 1 ≤ x. (a) Does the density function f(x) of X exist? If yes, find f(x), if not, why not? Compute: (b) P(-1/2 < X ≤1/2 ); (c) P(X ≥ 0); (d) What is the median of X? (e) Is the median of X unique?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...
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2. Suppose the random variable X has the cdf F(x) = 0, x < −1, = (x+2)/4, −1 ≤ x < 1, = 1, 1 ≤ x. (a) Does the
density function f(x) of X exist? If yes, find f(x), if not, why not? Compute: (b) P(-1/2 < X ≤1/2 ); (c) P(X ≥ 0);
(d) What is the median of X? (e) Is the median of X unique?
Transcribed Image Text:2. Suppose the random variable X has the cdf F(x) = 0, x < −1, = (x+2)/4, −1 ≤ x < 1, = 1, 1 ≤ x. (a) Does the density function f(x) of X exist? If yes, find f(x), if not, why not? Compute: (b) P(-1/2 < X ≤1/2 ); (c) P(X ≥ 0); (d) What is the median of X? (e) Is the median of X unique?
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