Question

Var(X), where X is any random variable, is equals to:

Select one:
a. E(X2)-(E(X))2
b. None of the above
c. (E(X))2
d. E(X2)
e. E(X2)+(E(X))2



Note: Answer E is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.

Answer 1

The correct answer is option (a): Var(X) = E(X^2) - (E(X))^2.

The variance of a random variable X is defined as the average of the squared differences between each value of X and its expected value (E(X)). Mathematically, it can be expressed as Var(X) = E((X - E(X))^2).

Expanding the squared term, we have Var(X) = E(X^2 - 2XE(X) + (E(X))^2). Distributing and rearranging, we get Var(X) = E(X^2) - 2E(X)E(X) + (E(X))^2. Simplifying, we obtain Var(X) = E(X^2) - (E(X))^2.