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Unformatted text preview: Administration Midterm regrades due by November 28th after lecture. CS70: Satish Rao: Lecture 33. Continuous Probability 1. Normal (Gaussian) Distribution. 2. Joint distributions. 3. Buffons needle. 4. Begin inference. Normal Distribution. For any and , a normal random variable has pdf f ( X ) = 1 2 2 e ( x ) 2 / 2 2 . Standard normal has = and = 1 . 2 2 . 2 . 4 Also is Gaussian distribution. Central limit theorem. Law of Large Numbers: For any set of independent identically distributed random variables, X i , A n = 1 n X i tends to the mean. Say X i have expecation = E ( X i ) and variance 2 . Mean of A n is , and variance is 2 n . Let A n = A n / n . E ( A n ) = 1 / n ( E ( A n ) ) = . Var ( A n ) = 1 2 / n Var ( A n ) = 1 . Central limit theorem: As n goes to infinity the distribution of A n approaches the standard normal distribution....
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This note was uploaded on 02/29/2012 for the course COMPSCI 70 taught by Professor Rau during the Fall '11 term at University of California, Berkeley.
 Fall '11
 Rau

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