Question

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.

Answer 1

a) 1

b) 1

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) =
`(1)/(\lambda)`

or

E(X) =
`(1)/(1)`

or

E(X) = 1

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

i.e

σₓ =
`\sqrt{(1)/(\lambda^2)}`

or

σₓ =
`\sqrt{(1)/(1^2)}`

or

σₓ = 1