Which of the following statements about the expected value E of random…
2025
Which of the following statements about the expected value E of random variables is always true ?
- A.
E (X + Y) = E (X) · E (Y)
- B.
E (tX) = t E (X), where t is a number
- C.
E (X + Y) = E (X) + E (Y) only if X and Y are independent
- D.
E (X1 + X2 + ... + Xn) = 1/n Σ (i=1 to n) E(Xi)
Attempted by 5 students.
Show answer & explanation
Correct answer: B
The expected value (or mean) of a random variable follows the property of linearity. One of the fundamental properties of linearity is the Homogeneity property:
For any random variable X and any constant (number) t, the expected value of tX is equal to t times the expected value of X.
Mathematically: E(tX) = tE(X).
This holds true regardless of the distribution of X.