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Math Help - 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
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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 \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.
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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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