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Let fi12(x1|r2) = c1£1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2(x2) = c2xź, 0 < x2 < 1, zero elsewhere, denote, respectively, the conditional pdf of X1 given X2 = x2, and the marginal pdf of X2. Determine (a) The constants c1 and c2. (b) The joint pdf of X1 and X2. (c) P(1/4 < X1 < 1/2|X2 = 5/8). (d) P(1/4 < X1 < 1/2).

Let fi12(x1|r2) = c1£1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2(x2) = c2xź, 0 < x2 < 1, zero elsewhere, denote, respectively, the conditional pdf of X1 given X2 = x2, and the marginal pdf of X2. Determine (a) The constants c1 and c2. (b) The joint pdf of X1 and X2. (c) P(1/4 < X1 < 1/2|X2 = 5/8). (d) P(1/4 < X1 < 1/2).

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. Let fi12(x1|x2) = c1¤1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2 (x2) = c20%, 0 < x2 < 1, zero elsewhere, denote, respectively, the conditional pdf of X1 given X2 = x2, and the marginal pdf of X2. Determine (a) The constants c1 and c2. (b) The joint pdf of X1 and X2. (c) P(1/4 < X1 < 1/2|X2 = 5/8). (d) P(1/4 < X1 < 1/2).
Transcribed Image Text:2. Let fi12(x1|x2) = c1¤1/x3, 0 < x1 < x2 < 1, zero elsewhere, and f2 (x2) = c20%, 0 < x2 < 1, zero elsewhere, denote, respectively, the conditional pdf of X1 given X2 = x2, and the marginal pdf of X2. Determine (a) The constants c1 and c2. (b) The joint pdf of X1 and X2. (c) P(1/4 < X1 < 1/2|X2 = 5/8). (d) P(1/4 < X1 < 1/2).
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