18.44 Lecture Notes - Lecture 12: Random Variable, Taylor Series, Binomial Theorem
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Key idea for all these examples: divide time into large number of small increments. Assume that during each increment, there is some small probability of thing happening (independently of other increments). The number e is de ned by e = lim (1 + 1/n) It"s the amount of money that one dollar grows to over a year when you have an interest rate of 100 percent, continuously compounded. It"s also the amount of money that one dollar grows to over years when you have an interest rate of 100 percent, continuously compounded. Can also change sign: e = lim (1 /n) Bernoulli random variable with n large and np = . Say = 2 or = 3. Let n be a huge number, say n = 106. Suppose i have a coin that comes up heads with probability /n and i toss it n times. Let k be some moderate sized number (say k = 4).
