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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0 X < 0 F(X): x² = 0 ≤ x < 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration μ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) 0 ≤ x < 4 otherwise (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0 X < 0 F(X): x² = 0 ≤ x < 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration μ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) 0 ≤ x < 4 otherwise (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0 X < 0 F(X): x² = 0 ≤ x < 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration μ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) 0 ≤ x < 4 otherwise (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].
Transcribed Image Text:Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. 0 X < 0 F(X): x² = 0 ≤ x < 4 16 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 2). (b) Calculate P(1.5 ≤ X ≤ 2). (c) Calculate P(X > 2.5). (d) What is the median checkout duration μ? [solve 0.5 = F(M)]. (e) Obtain the density function f(x). f(x) = F'(x) (f) Calculate E(X). (g) Calculate V(X) and σx. V(X) 0 ≤ x < 4 otherwise (h) If the borrower is charged an amount h(x) = x² when checkout duration is X, compute the expected charge E[h(X)].
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