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Math Help - Question on exponential distribution

  1. #1
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    Question on exponential distribution

    Let {X1,...,Xn} be a random sample from the exponential distribution with probability density function f(x) = (mu)^-1 exp(-x/mu) for x > 0, and 0 otherwise, where mu>0 is an unknown parameter.
    a) Compute the mean and the variance of Xi.

    Any help would be greatly appreciated
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  2. #2
    Senior Member Sambit's Avatar
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    Re: Question on exponential distribution

    Just try the usual integration \int_{0}^{\infty} xf(x) dx for mean and \int_{0}^{\infty} x^2f(x) dx for variance.
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  3. #3
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    Re: Question on exponential distribution

    Hi, I did this and found that E(X)=mu, and Var(X)=mu^2. So, would E(Xi) be the sum from i=1 to k of mu i, and would Var(Xi) be the sum from i to k of (mu i)^2?
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  4. #4
    Senior Member Sambit's Avatar
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    Re: Question on exponential distribution

    \mu and \mu^2 are E(X_i) and Var(X_i) respectively. The summation will come in the answer if you want E(\sum_{i=1}^{n} X_i) and Var(\sum_{i=1}^{n} X_i)
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