Expected Value-to calculate the expected value of a probability distribution?

Question

* important note: the U used here means "mu" there is no symbol on keyboard for it)


Question:
You invest $10,000 in the Stock Market. The rate is -$10,000 30% of the time. $10,000 20% of the time. Find the expected or average return.

Given:

x -10 10 20 (in thousands $)
P9X=x) 0.3 0.2 0.5



Please solve and show work, thanks.

oops error
I mean P(X=x)

Answer 1

Expected value = Σ (value/return)*(probability)

So (-10k)*(0.3) + (10k)*(0.2) + (20k)*(0.5) = 9k

Answer 2

oh man. i hate proofs....senior right now and im taking calculas 2 and yet, i still kinda struggle with rpoofs.

sorry i'll just help u on the others. proofs aint my thing