2. Consider independent fair coin tosses: P(X; = 1) = P(Xį = 0) = 12. Let Ăn = ½/2 Σï=₁ Xį be the sample mean of first n coin tosses. n (a) What is the E[X100]? (b) What can you say about the probability that the sample mean X100 lies between 40 and 60?

2. Consider independent fair coin tosses: P(X; = 1) = P(Xį = 0) = 12. Let Ăn = ½/2 Σï=₁ Xį be the sample mean of first n coin tosses. n (a) What is the E[X100]? (b) What can you say about the probability that the sample mean X100 lies between 40 and 60?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.2: Introduction To Probability

Problem 66E

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Question

2. Consider independent fair coin tosses: P(X; = 1) = P(Xį = 0) = 2. Let
X₁ = 1/2₁ X₁ be the sample mean of first n coin tosses.
n
(a) What is the E[X100]?
(b) What can you say about the probability that the sample mean X100 lies
between 40 and 60?

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