**2. Correct. The answer is true**

Applying the definition of expectation for a continuous random variable:

*E(**Y)* = ∫_{0}^{∞} *yf**(y)dy*

*E(**Y)* = ∫_{0}^{∞} *y(2e ^{-2y})^{
}dy*

*E(**Y)* = 2 [ *ye ^{-}*

*E(Y)* = 1/2(equivalent to 500 barrels of oil)

Regarding E(Y^{2}),
we have that:

*E(**Y ^{2})* = ∫

*E(**Y ^{2})* = 2∫

*E(**Y ^{2})* = 2 [

*E(**Y ^{2})* = 1/2