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Consider some Poisson random variable, .
Let be the expectation of , and let be the variance of . Recall that if a random variable has a Poisson distribution, then:
Now, we'll use the following property of expectation and variance for any random variable, :
So, for any random variable having a Poisson distribution, the above result can be rewritten as:
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Day 5: Poisson Distribution II
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Consider some Poisson random variable, . Let be the expectation of , and let be the variance of . Recall that if a random variable has a Poisson distribution, then:
Now, we'll use the following property of expectation and variance for any random variable, :