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¡.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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