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 +2 F(x) = 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). 0.25 (b) Calculate P(1.5 ≤ x ≤ 2). 0.1094 (c) Calculate P(X > 2.5). 0.6094 (d) What is the median checkout duration ? [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 σ, V(X) 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 +2 F(x) = 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). 0.25 (b) Calculate P(1.5 ≤ x ≤ 2). 0.1094 (c) Calculate P(X > 2.5). 0.6094 (d) What is the median checkout duration ? [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 σ, V(X) 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)].
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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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.
0
x < 0
+2
F(x) =
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).
0.25
(b) Calculate P(1.5 ≤ x ≤ 2).
0.1094
(c) Calculate P(X > 2.5).
0.6094
(d) What is the median checkout duration ? [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 σ,
V(X)
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)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fb7206e-115e-4b4d-a1f2-25e3abb72135%2Fcfb4aae2-7a9a-4a9d-bcf5-2ee6e1cda33c%2Ff2m1up2_processed.png&w=3840&q=75)
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
+2
F(x) =
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).
0.25
(b) Calculate P(1.5 ≤ x ≤ 2).
0.1094
(c) Calculate P(X > 2.5).
0.6094
(d) What is the median checkout duration ? [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 σ,
V(X)
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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