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Let X be the time in minutes between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1, compute the following: (If necessary, round your answer to three decimal places.)

(a) The expected time between two successive arrivals is minutes.

(b) The standard deviation of the time between successive arrivals is minutes.

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Respuesta :

Answer:

a) 1

b) 1

Step-by-step explanation:

Data provided in the question:

X = The time in minutes between two successive arrivals

X has an exponential distribution with λ = 1

Now,

a) The expected time between two successive arrivals is minutes i.e

E(X) = [tex]\frac{1}{\lambda}[/tex]

or

E(X) = [tex]\frac{1}{1}[/tex]

or

E(X) = 1

b)  The standard deviation of the time between successive arrivals is minutes

i.e

σₓ = [tex]\sqrt{\frac{1}{\lambda^2}}[/tex]

or

σₓ = [tex]\sqrt{\frac{1}{1^2}}[/tex]

or

σₓ = 1

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