Question

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, compute the following:

a) The expected time between two successive arrivals

b) The standard deviation of the time between success arrivals

c) Calculate the probability P (X≤3)

d) Calculate the probability P(2≤X≤5)

Answer 1

(a)

Distribution of X = the time between two successive arrivals at the drive-up window of a local bank is an exponential distribution with λ=1 and is given by:

,

               for x > 0

The expected time between two successive arrivals = Mean value of X =

So,

Answer is:

1

(b)

The standard deviation of the time between success arrivals =

So,

Answer is:

1

(c)

between limits 0 to 3.

Applying limits, we get:

So,

Answer is:

0.9502

(d)

between limits 2 to 5

Applying limits, we get:

So,

Answer is:

0.1286