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Unformatted text preview: < it skewed to the right (see next gure). 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 2.5 x f(x) Beta distribution densities with parameters and < = 6 , = 4.5 = 1.5 , = 3 Even though x was dened in the interval 0 x 1, its use can be extended to random variables dened over some nite interval, c x d . In this case we can simply rescale the variable using y = x-c d-c , and y will be between 0 and 1. It can be shown that B ( , ) = ( )( ) ( + ) . Using this relation between the beta and gamma functions we can nd the mean and variance of the beta distribution: E ( X ) = + and var ( X ) = ( + ) 2 ( + + 1) . 2...
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This note was uploaded on 01/14/2011 for the course STATS 100A taught by Professor Wu during the Fall '07 term at UCLA.
- Fall '07