Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.F(x)==0x²251X<00 4.5).5≤XUse the cdf to obtain the following. (If necessary, round your answer to four decimal places.)(a) Calculate P(X ≤ 4),(b) Calculate P(3.5 ≤ x ≤ 4).(d) What is the median checkout duration ? [solve 0.5 = F(p)]. (e) Obtain the density function f(x).f(x)F'(x)=(f) Calculate E(X).(g) Calculate V(X) andV(X)0≤x<5otherwise(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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Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 x² 25 1 x < 0 0≤x<5 (c) Calculate P(X> 4.5). 5 ≤x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 4). (b) Calculate P(3.5 ≤ x ≤ 4).

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 x² 25 1 x < 0 0≤x<5 (c) Calculate P(X> 4.5). 5 ≤x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X ≤ 4). (b) Calculate P(3.5 ≤ x ≤ 4).

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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Question

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
F(x)=
=
0
x²
25
1
X<0
0<x<5
(c) Calculate P(X > 4.5).
5≤X
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X ≤ 4),
(b) Calculate P(3.5 ≤ x ≤ 4).
(d) What is the median checkout duration ? [solve 0.5 = F(p)].

(e) Obtain the density function f(x).
f(x)
F'(x)
=
(f) Calculate E(X).
(g) Calculate V(X) and
V(X)
0≤x<5
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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