Problem #10: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random variable with the following pdf. f(x) = 10 (1-x/79)8 0 < x < 79 otherwise If you use this crossing every day for the next 7 days, what is the probability that you will wait for at least 10 seconds on exactly 4 of those days?
Problem #10: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random variable with the following pdf. f(x) = 10 (1-x/79)8 0 < x < 79 otherwise If you use this crossing every day for the next 7 days, what is the probability that you will wait for at least 10 seconds on exactly 4 of those days?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:Problem #10: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street crossing is a random
variable with the following pdf.
Problem #10:
f(x) =
(1-x/79)8 0≤x < 79
otherwise
{*ª
If you use this crossing every day for the next 7 days, what is the probability that you will wait for at least 10
seconds on exactly 4 of those days?
Round your answer to 4 decimals.
Expert Solution

Step 1
Solution - Given that , Let X denote the waiting time (in seconds) for the pedestrian signal at a perticular streer crossing is a random variable with th following pdf
f(x)=9/79(1-x/79)8 for 0≤x≤79
Also given that n=7 (# of days) then find
P(X=4)=?
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