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You flip a coin 25 times. Let X; be the Bernoulli random variable indicating if the i-th coin flip lands on a head. 1, X; = 10, if the i-th coin flip lands on a head, 0, otherwise. Assume that the probability of each coin flip landing on a head is 0.5, and that the 25 coin flips are independent. (a) Are X1, X2, ..., X25 i.i.d. (independent and identically distributed)? Briefly explain. (b) Find the expected value of X1 + X, + .…+X25 ... 25 (c) Find the variance of X. (Hint: first compute the variance of X¡.)

You flip a coin 25 times. Let X; be the Bernoulli random variable indicating if the i-th coin flip lands on a head. 1, X; = 10, if the i-th coin flip lands on a head, 0, otherwise. Assume that the probability of each coin flip landing on a head is 0.5, and that the 25 coin flips are independent. (a) Are X1, X2, ..., X25 i.i.d. (independent and identically distributed)? Briefly explain. (b) Find the expected value of X1 + X, + .…+X25 ... 25 (c) Find the variance of X. (Hint: first compute the variance of X¡.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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You flip a coin 25 times. Let X; be the Bernoulli random variable indicating if the i-th coin flip lands on a head. 1, X; = | 0, otherwise. if the i-th coin flip lands on a head, Assume that the probability of each coin flip landing on a head is 0.5, and that the 25 coin flips are independent. (a) Are X1, X2, ..., X25 i.i.d. (independent and identically distributed)? Briefly explain. (b) Find the expected value of X1 + X, + .…+X25 ... 25 (c) Find the variance of X. (Hint: first compute the variance of X¡.)
Transcribed Image Text:You flip a coin 25 times. Let X; be the Bernoulli random variable indicating if the i-th coin flip lands on a head. 1, X; = | 0, otherwise. if the i-th coin flip lands on a head, Assume that the probability of each coin flip landing on a head is 0.5, and that the 25 coin flips are independent. (a) Are X1, X2, ..., X25 i.i.d. (independent and identically distributed)? Briefly explain. (b) Find the expected value of X1 + X, + .…+X25 ... 25 (c) Find the variance of X. (Hint: first compute the variance of X¡.)
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