ECON2209 Lecture 13: 22February_EconStats_Karagodsky
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1 cupcake problem: sell for , costs per cupcake to make, must make them in advance, demand is usually normally distributed about n(500, 400) P (x > x0)(p c) + p (x < x0)( c) P (x x0)(5 2) 2p (x < x0) 3 5p (x < x0) = 0 solve for x0. E[p rof it] = p r(x x0)(p c) + p r(x < x0)( c) = 3[1 p (x < x0)] 2p (x < x0) = . 25 (from the chart using . 6 to trace back to the z) Approximately normally distributed if np(1-p) > 5. ie, if the number of itera- tions is large it will look more and more normal. Binomial: x = x1 + x2 + + xn, e(xi) = p, var(x) = p(1-p, e[x] = np, var[x] = np(1-p) ex: n = 100, p = . 5. E[x] = np = 50 var(x) = np(1-p) = 25 (higher than 5, imporant to check)