Unformatted text preview: neously. 3. Exponential distribution. X is an exponential distribution with parameter Î» if the density function is f ( x ) = Î»eÎ»x for x â‰¥ . It can be shown that X = 1 Î» , V X = 1 Î» 2 . 4. Given random sample X 1 , Â·Â·Â· ,X n , the likelihood function is given as the product of probability or density functions, i.e. L ( Î¸ ) = f ( x 1 ; Î¸ ) f ( x 2 ; Î¸ ) Â·Â·Â· f ( x n ; Î¸ ) . The maximum likelihood estimatate of Î¸ is an estimate that maximizes L ( Î¸ ) . If we denote Ë† Î¸ = Î¸ ( x 1 , Â·Â·Â· ,x n ) to be the maximum likelihood estimate, The maximum likelihood estimator (MLE) of Î¸ is denoted by Ë† Î¸ = Ë† Î¸ ( X 1 , Â·Â·Â· ,X n ) . Review Problems. Example 6.12. Example 6.16. Example 6.17....
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 Fall '04
 Chung
 Statistics, Normal Distribution, probability density function, Estimation theory, random sample X1, [email protected], Moo K. Chung

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