Question
Download Solution PDFIf a random variable X following Poisson distribution has expectation λ, then which of the following statements is true?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFA random variable X is given that follows a Poisson distribution with parameter λ, which represents the expected number of events in an interval. The probability mass function (PMF) of a Poisson-distributed random variable is given as follows:
Therefore, we can write:
Taking the ratio of these two probabilities, we have:
Rearranging the above equation gives us the relation between the two probabilities:
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