Exercise 7: Suppose upon arriving at a bus stop, the number of minutes you have to wait for a bus to arrive is given by the probability density function: (c(10 – x)², 0, 0

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Exercise 7: Suppose upon arriving at a bus stop, the number of minutes you have to wait for a bus to arrive
is given by the probability density function:
(c(10 – x)²,
0,
0 <x < 10
f(x) =
otherwise.
(a) What is the value of c? (Hint: This requries appealing to the second bullet point in the definition
of a probability density function.)
(b) What is the probability you have to wait more than 8 minutes for the bus?
(c) What is the expected value on the number of minutes you have to wait?
(d) What is the variance on the number of minutes you have to wait?
Transcribed Image Text:Exercise 7: Suppose upon arriving at a bus stop, the number of minutes you have to wait for a bus to arrive is given by the probability density function: (c(10 – x)², 0, 0 <x < 10 f(x) = otherwise. (a) What is the value of c? (Hint: This requries appealing to the second bullet point in the definition of a probability density function.) (b) What is the probability you have to wait more than 8 minutes for the bus? (c) What is the expected value on the number of minutes you have to wait? (d) What is the variance on the number of minutes you have to wait?
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