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=0.5, compute the following: (If necessary, round your answer to three decimal places.) 

(a) The expected time between two successive arrivals is 

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

(c) P(X≤4) 

(d) P(1≤X≤3) 

(e) P(X≥1.5) 

Answer 1

Here we have exponential distribution with   = 0.5

a. Expected time :

b. Standard deviation :

Standard deviation =

CDF of exponential distribution is

F(x) =p ( X x ) =   

c.

p ( x 4 )

=

= 1 - e^-2

^{= 1 - 0.1353}

^{= 0.8647}

^{d. p ( 1} x 3 )

= p ( x 3 ) - p ( x 1 )

= $1-e^{-0.5*3}$ -

=

= - 0.2231 + 0.6065

= 0.3834

e) p ( x 1.5 )

= 1 - p ( x 1.5 )

= 1 - $(1-e^{-0.5*1.5})$

= $e^{-0.5*1.5}$

= 0.4724