For any X € L = L^1 prove that |EX| ≤ E|X|
For any X € L = L^2 prove that |EX|^2 ≤ E|X|^2
I was trying to prove those facts but I was not sure how to...
I figured out that I need to use the cauchy schwarz inequality but i did not clearly understand how to apply it
I started the questions like this for the first one,
a ∙ b ≤ |a ∙ b| ≤ |a||b|
I started the questions like this for the second one,
var (X) = E(X^2)-(EX)^2
but this is how far I came, can someone plz help me?