Let be a Poisson process with rate and . Prove the following: (a) for and i.e. the conditional distribution of given is Bin (b) for
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Originally Posted by BrooketheChook Let be a Poisson process with rate and . Prove the following: (a) for and i.e. the conditional distribution of given is Bin (b) for What did you try for (a)? If you write the definition of conditional probability, this should go easily. For (b), a hint (yes it is) is: .
For (a) I get Maybe its because im really tired, but I cant see how this leads to
Originally Posted by BrooketheChook For (a) I get Maybe its because im really tired, but I cant see how this leads to Many a simplification happens here. The exponentials simplify, and so do the terms with lambda. It remains .
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