If the conditional density of $Y$ given by $X=x$ is given by
$$f(y/x) = \left\{ \begin{array}{ll} \binom{5}{y} x^y (1-x)^{5-y} & \mbox{if $y = 0,1,2,...,5$};\\ 0 & \mbox{otherwise}.\end{array} \right. $$
and the marginal density of $X$ is
$$f_1(x) = \left\{ \begin{array}{ll} 4x^3 & \mbox{if $0<x<1$};\\ 0 & \mbox{otherwise}.\end{array} \right. $$
then what is the conditional expectation of $Y$ given the event $X=x$?
Thank you, any help will be appreciated.