Question

Read this E[2X^2 â€" Y].

Answer 1

Looks like a badly encoded/decoded symbol. It's supposed to be a minus sign, so you're asked to find the expectation of 2X ² - Y.

If you don't know how X or Y are distributed, but you know E[X ²] and E[Y], then it's as simple as distributing the expectation over the sum:

E[2X ² - Y] = 2 E[X ²] - E[Y]

Or, if you're given the expectation and variance of X, you have

Var[X] = E[X ²] - E[X]²

→   E[2X ² - Y] = 2 (Var[X] + E[X]²) - E[Y]

Otherwise, you may be given the density function, or joint density, in which case you can determine the expectations by computing an integral or sum.