Answer:
Explanation:
False.
The expected value of the sum of two random variables X and Y is always equal to the sum of their individual expected values, E(X) and E(Y), regardless of their correlation. That is, E(X + Y) = E(X) + E(Y).
The covariance of X and Y, which is a measure of their linear association or correlation, is given by Cov(X, Y) = E[(X - E(X))(Y - E(Y))]. The correlation between X and Y, denoted by ρ(X, Y), is defined as the covariance between X and Y divided by the product of their standard deviations, that is, ρ(X, Y) = Cov(X, Y) / (σ(X)σ(Y)).
The correlation between X and Y can affect their joint distribution and the probability of certain outcomes, but it does not affect the expected value of their sum. Therefore, the statement that E(X + Y) is equal to the sum of their individual expected values minus their correlation is false.