Question

If \( X \) is a random variable such that \[ P(X = -2) = P(X = -1) = P(X = 2) = P(X = 1) = \frac{1}{6}, \quad P(X = 0) = \frac{1}{3}, \] then the mean of \( X \) is:

• A. \( \frac{5}{3} \)
• B. \( 1 \)
• C. \( 0 \)
• D. \( \frac{3}{5} \)

Hint:

Symmetry in distribution with equal probabilities often results in a mean of zero.

Answer 1

The Correct Option is C

The mean of a discrete random variable is given by: \[ \mu = \sum x_i \cdot P(x_i) \] Substitute: \[ \mu = (-2)\cdot \frac{1}{6} + (-1)\cdot \frac{1}{6} + 0\cdot \frac{1}{3} + 1\cdot \frac{1}{6} + 2\cdot \frac{1}{6} = \frac{-2 -1 + 1 + 2}{6} = \frac{0}{6} = 0 \]