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Solved: Let X =the time between two successive arrivals at
Chapter 4, Problem 59E(choose chapter or problem)
Problem 59E
Let X =the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1(which is identical to a standard gamma distribution withα = 1 ), compute the following:
a. The expected time between two successive arrivals
b. The standard deviation of the time between successive arrivals
c. P(X ≤ 4)
d. P( 2 ≤ X ≤ 5 )
Questions & Answers
QUESTION:
Problem 59E
Let X =the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1(which is identical to a standard gamma distribution withα = 1 ), compute the following:
a. The expected time between two successive arrivals
b. The standard deviation of the time between successive arrivals
c. P(X ≤ 4)
d. P( 2 ≤ X ≤ 5 )
ANSWER:
Answer :
Step 1:
Let X =the time between two successive arrivals at the drive-up window of a local bank.
If X has an exponential distribution with λ = 1.
The exponential pdf is a special case of the general gamma pdf in which and
has been replaced
.
The mean of the formula is given
The variance of the formula is given by,
Then,standard is a square root of the variance.
a).
X = time between two successive arrivals (assumed units is hours) X ~ Exp (l = 1).
The expected time between two successive arrivals is
The mean of the formula is given
Therefore the expected time between two successive arrivals is 1 hour.