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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 and variance 2 , Then we have W= n X / -= 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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