Hi!

I have the following problem:

Suppose X ~ Poisson (Lambda). Show P(X > 2lambda) =< 1/lambda

So I wrote out Chebshev's by definition:

P(|X - u| > t) =< V(x)/t^2

I made a simple substitution of t = lamda and proceeded.

P(|X-lamda| > lamda) = P(X > 2lambda) = lambda/lambda^2 =< 1/lambda

Does this make sense?