Question: Suppose X is a Poisson-distributed random variable. Can three different values of X have equal probabilities? (The answer is no, you have to first prove

Suppose X is a Poisson-distributed random variable. Can three different values of X have equal probabilities?

(The answer is "no, you have to first prove that if three such values exist, they must be consecutive integers.")

please give explaination on this question

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