Question

The p.m.f. of a random variable \( X \) is: \[ P(X) = \frac{2x}{n(n+1)}, \quad x = 1, 2, 3, \ldots, n \] \[ P(X) = 0, \quad \text{Otherwise.} \] Then \( E(X) \) is:

• A. \( \frac{n+1}{3} \)
• B. \( \frac{2n+1}{3} \)
• C. \( \frac{n+2}{3} \)
• D. \( \frac{2n-1}{2} \)

Hint:

For discrete random variables, calculate \( E(X) \) by summing \( x \cdot P(X = x) \), and use known summation formulas for efficiency.