Question

Suppose X takes the values -10 and 20 with probability 1/4 and 3/4 respectively, calculate E[X²].

• A. 225
• B. 275
• C. 325
• D. 375

Hint:

To calculate E[X²], square each value of X, multiply by its probability, and sum the results.

Answer 1

The Correct Option is C

To calculate \( E[X^2] \), we use the formula for the expected value of the square of a random variable:
\(E[X^2] = \sum P(X) \cdot X^2\)

Substitute the given values: \[ E[X^2] 
\(= \frac{1}{4} \cdot (-10)^2 + \frac{3}{4} \cdot 20^2\) 

\(E[X^2] = \frac{1}{4} \cdot 100 + \frac{3}{4} \cdot 400\)
\(= 25 + 300 = 325\)

 Thus, the correct answer is \(\text{(c)}. \)