We consider n independent tosses of a biased coin whose probability of heads, Y, is uniformly distributed over the interval [0.1, 0.8]. Let X be the number of heads obtained. (1) Let a and 3 be real numbers such that E[X|Y] = a Y+3. Derive the values of (a, 3). Derive E[X] and var(Y). (2) (3) Calculate the value of var(X).

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