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Suppose that X is a uniform random variable on the interval [0, 1]. After observing the value X = x, we generate a second random variable Y by picking a number uniformly at random from the interval [r, 1]. What is the marginal distribution of Y (i.e., fy (y))?

Suppose that X is a uniform random variable on the interval [0, 1]. After observing the value X = x, we generate a second random variable Y by picking a number uniformly at random from the interval [r, 1]. What is the marginal distribution of Y (i.e., fy (y))?

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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Suppose that \( X \) is a uniform random variable on the interval \([0, 1]\). After observing the value \( X = x \), we generate a second random variable \( Y \) by picking a number uniformly at random from the interval \([x, 1]\). What is the marginal distribution of \( Y \) (i.e., \( f_Y(y) \))?
Transcribed Image Text:Suppose that \( X \) is a uniform random variable on the interval \([0, 1]\). After observing the value \( X = x \), we generate a second random variable \( Y \) by picking a number uniformly at random from the interval \([x, 1]\). What is the marginal distribution of \( Y \) (i.e., \( f_Y(y) \))?
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