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).
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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2393a88-6b8c-41e1-9d25-6d49f7f7e10c%2F261d3277-cfb4-4f2c-8baa-8131c4ed23d3%2F6verea8_processed.jpeg&w=3840&q=75)
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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