Problems in Probability

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Fall 2011 Strategic Practice 5: Section 4 (LOTUS "Law of the Unconscious Statistician") - Question 1
For X ~ Pois(), find E(X!) (the average factorial of X), if it is finite.
Solution: For lambda between 0 and 1, by LOTUS we get, E(X!) = e^-lambda / (1 - lambda). Infinite for lambda greater than or equal to 1.
"Mathematics is the logic of certainty, but statistics is the logic of uncertainty."
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