Suppose we flip three fair coins. Let X = number of Heads.(a) Calculate the variance of X directly by using ONLY the PMF for X and theformula for variance (b) Calculate the variance again, but this time, use some of the tools from thebottom of page 9 (split X into 3 Bernoulli r.v.s).(c) Let Y = three times the Bernoulli r.v. for the first coin. Calculate Var(Y ).(d) Explain why your answer to Part C is different from Parts A and B.

Suppose we flip three fair coins. Let X = number of Heads.(a) Calculate the variance of X directly by using ONLY the PMF for X and theformula for variance (b) Calculate the variance again, but this time, use some of the tools from thebottom of page 9 (split X into 3 Bernoulli r.v.s).(c) Let Y = three times the Bernoulli r.v. for the first coin. Calculate Var(Y ).(d) Explain why your answer to Part C is different from Parts A and B.

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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