Question: Let X(t) be a Poisson process with rate . It is given that X(1) = n. Show that the conditional distribution of X(0.4) is binomial(n,

Let X(t) be a Poisson process with rate α. It is given that X(1) = n. Show that the conditional distribution of X(0.4) is binomial(n, 0.4). In words, if we know that n events occurred in the interval (0, 1], then the number of events that occurred in the interval (0, 0.4] is a binomial(n, 0.4) random variable.

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