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The uniform distribution is not directly in the tables, so I recommend you memorize the formulas for mean and variance. However, if d = 0, then the uniform distribution is a special case of a beta distribution with () = u, a=l,b=l. 2 Beta The probability density function of a beta distribution with () = l has the form C/ 4 Study Manual-!! 3. 5 a = 2, b = 1 o a=6,b=3 3 ·5 · <> a= 18, b = 9 t::,. 1: Probability density function of four beta distributions with 8 = 1 and mean 2/3 The parameters a and b must be positive.
L, a 2 ) to describe X. 95. 645 is a commonly used percentile of the normal distribution, and is listed at the bottom of the table you get at the exam. 3. BERNOUUI SHORTCUT 47 You should internalize the above reasoning so you don't have to write it out each time. Namely, to calculate a percentile of a random variable being approximated normally, find the value of x such that
You are given the following: X is a random variable with probability density function • x 2: fJ, a > 0, fJ > 0 • E[X] = 7500. • E[X2 ] =75,000,000. • m is the median of X. Determine the value off( m ). 20. 00035 [4-F00:32] You are given the following for a sample of five observations from a bivariate distribution: (i) (ii) X y 1 4 2 3 2 4 5 6 6 4 C. 8. A is the covariance of the empirical distribution Fe as defined by these five observations. B is the maximum possible covariance of an empirical distribution with identical marginal distributions to Fe.