18.44 Lecture Notes - Lecture 18: Plat
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Let"s plot this for a few values of n. If we replace fair coin with p coin, what"s probability to see k heads. Let"s plot this for p = 2/3 and some values of n. Seems to look like it"s converging to a curve. Say x is a (standard) normal random variable if f (x) = f(x) = This looks kind of tricky, but there happens to be a nice way to do it. Write i = e dx and then try to compute i as a two dimensional integral. That is, write i = e dx e dy = e dx e dy. Then switch to polar coordinates i = e r d dr = 2 r e dr = - 2 e so i = 2 . We have e[x] = xf(x)dx and we can see by symmetry that this is zero. We cam compute e[x] directly: e[x] = .
