Poisson distribution with a mean that is a uniform random variable

  1. It's been a while since I've taken probability so I'm not sure if I have this right:

    Question: "Suppose y|x is poisson with mean x and X ~ Uniform[0,5]. compute Pr[Y>=1]"

    Here is what I did: E[Y] = E[E(Y|X)] = E[X] = 2.5 = the parameter for poisson

    Pr[Y>=1] = 1 - Pr[Y = 0]

    = 1 - e^(-2.5)

    Is this right? It seems overly simple so I'm not sure...
    Last edited: Mar 4, 2010
  2. jcsd
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