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Unformatted text preview: Lecture 21 Fall 2005 2 Example: X1~N(693.2, 22820) and X2~N(631.7,19205), and X1 and X2 are independent. Find P(X1>X2). Central Limit Theorem If X1, X2, …, Xn are observations of a random sample of size n from a distribution with mean μ and variance σ 2 , Then we have W= n X / σ μ= n n X i∑ → N(0,1) as n →∞ In another word, W be can approximated by normal distribution when sample size n is sufficiently large. “sufficiently large”: n is greater than 20 Ping Ma Lecture 21 Fall 2005 3 Example : Let X be the mean of a random sample size 36 from an exponential distribution with mean 3. Approximate P(2.5< X <4) Ping Ma Lecture 21 Fall 2005 4 ...
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 Fall '05
 TBA
 Statistics, Central Limit Theorem, Normal Distribution, Variance, Probability theory, µ, 2 w

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