From [0]: Let X be a random variable and g be any function. If X is continuous, then the expectation of g(X) is defined as, E[g(X)] = \int_−∞^∞ g(x)f(x) dx,

From [0]: Let X be a random variable and g be any function. If X is continuous, then the expectation of g(X) is defined as, E[g(X)] = \int_−∞^∞ g(x)f(x) dx, where f is the probability density function of X. --- For us, with mean 3 and sigma 2/3, f = 3/2 e^(-9/8 (x-3)^2)/sqrt(2 π) We need to integrate numerically; using Wolfram [1] we get an estimate of 30.8099. If we ask for the expected value over the entire distribution we get 31. [0] http://imai.princeton.edu/teaching/files/Expectation.pdf http://imai.princeton.edu/teaching/files/Expectation.pdf [1] http://www.wolframalpha.com/input/?i=integrate+3%2F2+e%5E%28-9%2F8+%28x-3%29%5E2%29%2Fsqrt%282+%CF%80%29*x%5E3%2C+x+%3D+1+..+5 http://www.wolframalpha.com/input/?i=integrate+3%2F2+e%5E%28... [2] http://www.wolframalpha.com/input/?i=expected+value+of+x%5E3+if+x+is+normal+with+mean+3+and+standard+deviation+2%2F3 http://www.wolframalpha.com/input/?i=expected+value+of+x%5E3...