otherwise (f) Calculate E(X). 1.3333 (g) Calculate V(X) and o V(X) (h) If the borrower is charged an amount h(X) x2 when checkout duration is X, compute the expected charge E[h(X)]. %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 52E
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F,g,h
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.
x < 0
F(x) =
0sx< 4
16
Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)
(a) Calculate P(X < 3).
0.5625
(b) Calculate P(2.5 s X s 3).
0.1719
(c) Calculate P(X > 3.5).
0.2344
Type here to search
R.
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. x < 0 F(x) = 0sx< 4 16 Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.) (a) Calculate P(X < 3). 0.5625 (b) Calculate P(2.5 s X s 3). 0.1719 (c) Calculate P(X > 3.5). 0.2344 Type here to search R.
(C)
Caiculdle P(X> 3.5).
0.2344
(d) What is the median checkout duration p? [solve 0.5 = F(¤)].
2.8284
(e) Obtain the density function f(x).
f(x) = F'(x)
2x
0sx < 4
16
0.
otherwise
(f) Calculate E(X).
1.3333
(g) Calculate V(X) and o.
V(X)
(h) If the borrower is charged an amount h(X) = X² when checkout duration is X, compute the expected charge E[h(X)].
P Type here to search
口 $
Transcribed Image Text:(C) Caiculdle P(X> 3.5). 0.2344 (d) What is the median checkout duration p? [solve 0.5 = F(¤)]. 2.8284 (e) Obtain the density function f(x). f(x) = F'(x) 2x 0sx < 4 16 0. otherwise (f) Calculate E(X). 1.3333 (g) Calculate V(X) and o. V(X) (h) If the borrower is charged an amount h(X) = X² when checkout duration is X, compute the expected charge E[h(X)]. P Type here to search 口 $
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