3 ms·

Oy. Someone needs to revoke my math license. Thanks for the correction!

• dxbydt 13y ago
  My, my, 2 mistakes on a silly uniform distribution! You must atone for this sin. Explain what the volume would be if the side came from a normal distribution over [1,5] (ie. mean 3, sigma 2/3) Otherwise I will personally call the MAA director on my speed dial & haul your ass back to stat101 :) But seriously, you write rather well on Quora & I'm sure the crowd would want to know what happens to the volume were you to choose a normal distribution instead of a uniform, so I hope you respond.
  • Cogito 13y ago
    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...