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Finding the mean and variance

  1. May 19, 2010 #1
    in the exponential distribution we know that

    μ = 1/λ and σ = 1/λ^2

    also f(x) = λ*e^-λχ

    how can i find the mean (μ) using integrals?

    generally what we do is this

    we integrate from a point to another the x*f(x) (EX)

    And the variance is EX^2-(EX)^2

    but here we have no points, so how can i prove that the mean is 1/λ?
     
  2. jcsd
  3. May 19, 2010 #2

    gabbagabbahey

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    I assume that your distribution is defined for [itex]0\leq x<\infty[/itex]? If so, you integrate over that entire interval:

    [tex]\mu=\int_0^{\infty}xf(x)dx[/tex]
     
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