Writing Errands

3. A distribution which is useful for modelling count data has the following probabilityfunction:fX(x) =r + x ô€€€ 1xpr(1 ô€€€ p)xLet X be a random variable with this probability function.(a) Explain how X can be derived as the number of failures before the rth success,from a series of independent trials with probability of success p.(b) Hence or otherwise show that E(X) = r(1ô€€€p)p .(c) Show that as r ! 1 in such a way that E(X) = < 1 is constant, fX(x) tendstowards a common distribution which is a function of only.

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