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Beta distribution [2 P]

Show that the mean, variance, and mode of the beta distribution are given respectively by
$\displaystyle E[\mu]$ $\displaystyle =$ $\displaystyle \frac{a}{a+b}$  
$\displaystyle var[\mu]$ $\displaystyle =$ $\displaystyle \frac{ab}{(a+b)^2 (a+b+1)}$  
$\displaystyle mode[\mu]$ $\displaystyle =$ $\displaystyle \frac{a-1}{a+b-2}.$  



Haeusler Stefan 2010-01-26