Expected value and variance
Probability theory · Mathematics
Study notes
Q: A die is rolled. Let X be the outcome. Find E(X) and Var(X). E(X) = (1+2+3+4+5+6)/6 = 21/6 = 3.5. E(X^2) = (1+4+9+16+25+36)/6 = 91/6 = 15.167. Var(X) = 91/6 - (7/2)^2 = 91/6 - 49/4 = (182-147)/12 = 35/12 = 2.917. SD = sqrt(35/12) = 1.708.