E(X) = [-∞]\int[/∞] g(x).f(x) dx
let g(x) = X
E(X) = [-∞]\int[/∞] 1.f(x) dx
= 1. [-∞]\int[/∞] f(x) dx
= 1
P.S: [-∞]\int[/∞] is the integral of -infinity to infinity
expectation is the expected value or mean.
I have tried the first one using probability density function. but am not sure of my answer. while the others I have no idea how to attempt them
thank you
hello!
can any1 please help me with the following proofs? thanks
let X and Y be random variables. prove the following:
(a) if X = 1, then E(X) = 1
(b) If X ≥ 0, then E(X) ≥ 0
(c) If Y ≤ X, then E(Y) ≤ E(X)
(d) |E(X)|≤ E(|X|)
(e) E(X)= \sumP(X≥n)