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Stats distribution

  1. Jul 28, 2010 #1
    hey guys/gals i have been given this cw question however i spent ages and can't seem to get my head around it can some one give me a hand

    " the number N of wrecks in a particular area of sea off the Cornish coast has a poisson distribution with mean [tex]\propto[/tex] . the probability that a wreck is known is p . Let X denote the number of known wrecks

    (a) state the conditional distribution of X given N=n

    (b) Find the Marginal Distribution of X "

    thats the question now i think (a) has some hting to do with Binonial distribution

    but i am complety stummped on (b)

    any help would be great

    thanks
     
  2. jcsd
  3. Jul 28, 2010 #2

    lanedance

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    Homework Helper

    I would start by writing out the binomial distribution for
    P(X=x|N=n)

    the form for P(N=n) is also given

    if i remember right, the joint pdf can be given to be
    P(X=x, N=n) = P(X=x|N=n)P(N=n)

    from that you should be able to find the marginal distribution by summing over n
     
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