Chapters: Expected value & Variance of a continuous random variable **Q1.** A box is to be constructed so that its height is five inches and its base is \( Y \) inches by \( Y \) inches, where \( Y \) is a random variable described by the probability density function (pdf), \( f(y) = 6y(1-y) \), \( 0 < y < 1 \). Find the expected value of the volume of the box.---**Q2.** Let \( X \) be a random variable with the probability density function \( f(x) = 3(1-x)^2 \) when \( 0 \leq x \leq 1 \) and \( f(x) = 0 \) otherwise.**a.** Verify that \( f \) is a valid pdf.**b.** Find the mean and variance of \( X \).**c.** Find \( P(X \leq 1/2) \).**d.** Find \( P(X \leq 1/2|X \geq 1/4) \).

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Q1. A box is to be constructed so that its height is five inches and its base is Y inches by Y inches, where Y is a random variable described by the pdf, f(y) = 6y(1 – y), 0 < y < 1. Find the expected value of the volume of the box.

Q1. A box is to be constructed so that its height is five inches and its base is Y inches by Y inches, where Y is a random variable described by the pdf, f(y) = 6y(1 – y), 0 < y < 1. Find the expected value of the volume of the box.

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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