Probability Theory, Exercise, Solutions, Mathematics.
of a random variable 2. (a) The expected value of a fair six-sided die is (1+2+3+4+5+6)/6 = 3.5. (b) The variance of X is calculated as Σ((x_i — μ)² × P(x_i)), where μ is the expected value of X, and P(x_i) is the probability of x_i. The calculation yields a variance of (1/6)[(1–3.5)² + (2–3.5)² +