Question: how to calculate the probability of a continuous random variable?
Answer: A certain continuous random variable has a probability density function (PDF) given by: f ( x ) = C x ( 1 − x ) 2 , f(x) = C x (1-x)^2, f(x)=Cx(1−x)2, where x x x can be any number in the real interval [ 0 , 1 ] [0,1] [0,1]. Compute C C C using the normalization condition on PDFs.