How to evaluate the mean of a beta (a,b) random variable from its probi density function,you may consider $X=x \in (0,1)$.I tried to use integration but i am not sure how to reduce to most simplest form as a may not be a integer.
How to find out the mean of beta distribution
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1Write the integral formula for $E[X]$ and observe that except for the constant having the wrong value, that integral is the area under the pdf of a _different_ beta random variable $Y$ (i.e. with different parameters than $(a,b)$). So, write the integrand as $Af_Y(x)$ where $f_Y(x)$ is this new pdf and get that $E[X] = A\int_0^1 f_Y(x) \mathrm dx = A.$ – 2012-03-07