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

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.

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.

Re: Exponential Distribution Question

For number 2

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

In your case $\displaystyle \displaystyle x=1 ,\lambda = 0.4$

Re: Exponential Distribution Question

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

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.

All you need to get the correct answer is already posted in this thread.

P(one or more failures in a month)=1-P(no failures in a month)

CB