Suppose that X is the length of time (in minutes) that a customer queues in a bank. The probability density function of X is given by (36–x²) 144 0 < x < 6, fx(x) = {, otherwise. find E(X), the expected value of Xand interpret thisTOsult. Fina Fx(#), the cumulative distribution function of X. Given that a customer has been queuing for 3 minutes, find the con- ditional probability that this customer will be queuing for at least 5 minutes in total.

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Chapter1: Combinatorial Analysis
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Probability.

Suppose that X is the length of time (in minutes) that a customer queues
in a bank. The probability density function of X is given by
(36–x²)
144
0 < x < 6,
fx(x) = {
otherwise.
Find E(X), the expected value of X and interpret this result.
FIna Fx ("), he cumulative distribution function of X.
Given that a customer has been queuing for 3 minutes, find the con-
ditional probability that this customer will be queuing for at least 5
minutes in total.
Transcribed Image Text:Suppose that X is the length of time (in minutes) that a customer queues in a bank. The probability density function of X is given by (36–x²) 144 0 < x < 6, fx(x) = { otherwise. Find E(X), the expected value of X and interpret this result. FIna Fx ("), he cumulative distribution function of X. Given that a customer has been queuing for 3 minutes, find the con- ditional probability that this customer will be queuing for at least 5 minutes in total.
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