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Question involving pdf of change of variable

  1. Nov 7, 2009 #1
    A Geiger counter records the times at which radioactive particles are detected. However, if two particles occur within a short time θ of each other, the second one is not detected. Then, the probability density function of X, the time between successive recorded detections, is f(x) = k exp(−x/μ), for θ ≤ x < ∞.

    Find k and the expectation of X.

    Let Y be the smallest of a sample of n observations on X. Find the probability density function of Y .


    I managed the first part and got k = (1/μ)exp(θ/μ) and E(X) = θ + μ

    I'm not exactly sure how to begin the second part!? I know there are n x_i's in the range of X and that Y is the smallest of these x_i's, but then how do it write that? confused :s

    Any help would be great.
     
  2. jcsd
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