# How to find the lambda parameter for an exponential distribution.

• March 23rd 2013, 06:00 PM
mcleja
How to find the lambda parameter for an exponential distribution.
Hi all, i have to answer the following question:

Suppose that the lifetime, T for a electric motor follows an exponential distribution. If 6% of the motor fail within a year, find the lambda parameter for the exponential distribution.

I have no idea how to do this could anybody help me?

Thank you.
• March 23rd 2013, 06:02 PM
chiro
Re: How to find the lambda parameter for an exponential distribution.
Hey mcleja.

Hint: What does the lambda represent? (Think in terms of the mean and sample mean).
• March 23rd 2013, 07:10 PM
mcleja
Re: How to find the lambda parameter for an exponential distribution.
lambda represents the rate? but how do i get the rate from the question?
• March 23rd 2013, 07:17 PM
ButterflyM
Re: How to find the lambda parameter for an exponential distribution.
Quote:

Originally Posted by mcleja
lambda represents the rate? but how do i get the rate from the question?

That's the question. :-) You need to get $\lambda$, but you have all other parameters to put into the formula. From the question, you know the probability and you also know that it takes from 0 to 1 year. Then solve for $\lambda$ the only remaining variable in the formula for the cumulative distribution function.
• March 23rd 2013, 08:04 PM
mcleja
Re: How to find the lambda parameter for an exponential distribution.
so we have P(X<=x)=1-e^(-lambda*x), P(X<=x)=0.06? and x=1 (1 year?) is this correct?
• March 24th 2013, 02:45 AM
chiro
Re: How to find the lambda parameter for an exponential distribution.
Hint: If you have so many fail in one year, what does this mean for a given x and P(X <= x)?