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Let X be uniformly distributed over [0,1]. And for some c in (0,1), define Y = 1 if X>= c and Y = 0 if X < c. Find E[X|Y].

My main problem is that I am having difficulty solving for f(X|Y) since X is continuous (uniform continuous over [0,1]) while Y is discrete (takes values of 0 or 1 only)