5.8. Let X be a random variable that takes on values between 0 and c. That is, P{0 ≤X ≤ c} = 1. Show that Var (X) ≤ Hint: One approach is to first argue that E[X²] ≤ CE[X]
5.8. Let X be a random variable that takes on values between 0 and c. That is, P{0 ≤X ≤ c} = 1. Show that Var (X) ≤ Hint: One approach is to first argue that E[X²] ≤ CE[X]
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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How can I solve this question 5.8.?
![5.8. Let X be a random variable that takes on values between 0 and c. That
is, P{0 ≤X ≤ c} = 1. Show that
Var(X) < =²2
4
Hint: One approach is to first argue that
E[X²] ≤ CE[X]
and then use this inequality to show that
Var(X) ≤ c²[a(1-a)] where a =
E[X]
C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0618968-6b5a-406b-a92d-661b061825b7%2Fe2c395e7-a304-473d-b0c3-91094223ae1f%2F2w5q56_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.8. Let X be a random variable that takes on values between 0 and c. That
is, P{0 ≤X ≤ c} = 1. Show that
Var(X) < =²2
4
Hint: One approach is to first argue that
E[X²] ≤ CE[X]
and then use this inequality to show that
Var(X) ≤ c²[a(1-a)] where a =
E[X]
C
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