1. The problem statement, all variables and given/known data A small manufacturing firm sells 1 machine per month with 0.3 probability; it sells 2 machines per month with 0.1 probability; it never sells more than 2 machines per month. If X represents the number of machines sold per month and the monthly profit is 2X2 + 3X + 1 (in thousands of dollars), find the expected monthly profit. 2. Relevant equations 3. The attempt at a solution E(2X2 + 3X + 1) = ∑(2X2 + 3X + 1)f(x), x = 1, 2 = (2+3+1)(.3) + (8+6+1)(.1) = 1.8 + 1.5 = 3.3 3.3 * 1000 = $3,300 The answer in the back is $3,800. If I take my 3.3 and add the mean of E(X) = .3(1) + 2(.1) = 0.5, I get 3.8 * 1000 = $3,800. I'm not sure if this is coincidence or actually how you solve the problem. If it's how you solve the problem, I don't understand why you add the mean of X. If it's not the way you solve it, I'm not sure what to do and would like some hints (but not a solution -- if possible) as to where to go. Thanks.