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Thread: How to find the lambda parameter for an exponential distribution.

  1. #1
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    Question 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.
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  2. #2
    MHF Contributor
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    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).
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  3. #3
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    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?
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  4. #4
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    Re: How to find the lambda parameter for an exponential distribution.

    Quote Originally Posted by mcleja View Post
    lambda represents the rate? but how do i get the rate from the question?
    That's the question. :-) You need to get $\displaystyle \lambda$, 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 $\displaystyle \lambda$ the only remaining variable in the formula for the cumulative distribution function.
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  5. #5
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    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?
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  6. #6
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    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)?
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