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).

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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 + B. Derive the values of (a, 3).
Derive E[X] and var(Y).
(2)
(3)
Calculate the value of var(X).
Transcribed Image Text: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 + B. Derive the values of (a, 3). Derive E[X] and var(Y). (2) (3) Calculate the value of var(X).
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