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¡.)

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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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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