If $X$ is a poisson random variable with $\lambda =\frac{1}{15}$, what is the expected value of $X$ given $X > 15$ ? I should know this but it's been a while since my intro to probability class.
Asked
Active
Viewed 153 times
4
-
Is this relevant: https://math.stackexchange.com/questions/1709504/memoryless-property-for-poisson-distribution ? – G Tony Jacobs Dec 03 '17 at 19:50
-
The definition of the conditional expectation: $$E[X|A]=\frac{E[X \ I_A]}{P(A)}$$ $I$ is the indicator function. Can you figure out what $A$ is in your specific case is? – Shashi Dec 03 '17 at 19:57
-
Intuitively, because the distribution is falling rapidly when we are this much greater than the mean, the expectation will be $16+\epsilon$. You will almost never have $X \ge 17$ – Ross Millikan Dec 04 '17 at 02:08