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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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.
Q2. Let X be a random variable with pdf f (x) = 3(1 – x)² when 0 <
x <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 < 1/2).
d. Find P(X < 1/2|X > 1/4).
Transcribed Image Text: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. Q2. Let X be a random variable with pdf f (x) = 3(1 – x)² when 0 < x <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 < 1/2). d. Find P(X < 1/2|X > 1/4).
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