# Exponential Distribution Question

• Nov 4th 2011, 04:37 PM
Paymemoney
Exponential Distribution Question
Hi

Can someone help me how to answer the following questions:

1) The life in years of an integrated circuit follows an exponential distribution with mean 7. For ten such circuits operating independently what is the probability that at least two will be working after 8 years?

2) The number of computer failures in a large company has a Poisson distribution, mean 0.40 failures per month. What is the probability that at least 10 minutes will elapse before the next vehicle?

P.S
• Nov 4th 2011, 06:17 PM
awkward
Re: Exponential Distribution Question
Quote:

Originally Posted by Paymemoney
Hi

Can someone help me how to answer the following questions:

1) The life in years of an integrated circuit follows an exponential distribution with mean 7. For ten such circuits operating independently what is the probability that at least two will be working after 8 years?

2) The number of computer failures in a large company has a Poisson distribution, mean 0.40 failures per month. What is the probability that at least 10 minutes will elapse before the next vehicle?

P.S

1) See if you can find the probability p that a circuit will be working after 8 years. Then the total number of circuits working after 8 years has a Binomial distribution with parameters p and n=10.

2) This problem statement makes no sense. Maybe you should double-check it.
• Nov 4th 2011, 07:06 PM
Paymemoney
Re: Exponential Distribution Question
Quote:

Originally Posted by Paymemoney
Hi
2) The number of computer failures in a large company has a Poisson distribution, mean 0.40 failures per month. What is the probability that a computer failure will occur in the next month?

P.S

copied it wrong.
• Nov 4th 2011, 07:19 PM
pickslides
Re: Exponential Distribution Question
For number 2

Recall the poisson distribution has $\displaystyle p(x)= \frac{\lambda^x\times e^{-\lambda}}{x!}$

In your case $\displaystyle x=1 ,\lambda = 0.4$
• Nov 5th 2011, 01:14 AM
Paymemoney
Re: Exponential Distribution Question
the answer to problem 2) is 0.3297 however what i get is 0.268. Is the answers wrong?
• Nov 5th 2011, 02:20 AM
CaptainBlack
Re: Exponential Distribution Question
Quote:

Originally Posted by Paymemoney
the answer to problem 2) is 0.3297 however what i get is 0.268. Is the answers wrong?

The book is right. If you want more help tell us how you got your answer.