Exponential PDFS

Taka

New Member
#1
Hey, I need some help with the below questions, any help would be great. Thanks.

The length of time in minutes, Y, that a customer spends in line at a bank teller’s window before being served is described by the exponential pdf f(y) = 0.2exp(-0.2y) y>0.

a) What is the median (m) waiting time in minutes and seconds?

Is this 0.2 = 1/m thus m = 5?

b) What is the probability that a customer will wait more than 10 minutes? Answer correct to 3 decimal places.

Do I just replace y with 10 here? Thus -0.4

c) Suppose the customer will leave if the wait is more than 10 minutes. Assume that the customer goes to the bank twice next month. Let the random variable X be the number of times in the next month that the customer leaves without being served. Find P(X=1) correct to 3 decimal places.

I'm not sure about this one at all.
 

mp83

TS Contributor
#4
You have to integrate you pdf with respect to x,i.e you get for an exponential Pr(X<=x)=1-exp(-.2x) . Its derivative is the pdf.

Try search the forum and you'll get this problem solved,it's a really common one.I think i replyed for the median time.
 

Taka

New Member
#5
So for:

b) P( y > 10) = ∫ 0.2exp-0.2y dy
= [ -e-0.2y ] Between 10 and infinity.
= e-2
= 0.135 (3 d.p.)
Yes?

But what about a) and c) ?
 

mp83

TS Contributor
#7
You gor it.

c is a common textbook problem.Use a distribution to find a probability (b) and then use it as the probabality of a binomial problem.Two trials with Pr(X>10)