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?