i) Let X ~Binom(100, 1/4 ). Find a, b 2 R so that Y = aX + b has expected value 0 and variance 1. (ii) Let X1,X2, . . . independent random variables with Bernoulli( 1/3 )‐distribution. Let n Sn := Σ Xi. i=1 Find a, b 2 R so that Y = aS20 + b has expected value 0 and variance 1.

i) Let X ~Binom(100, 1/4 ). Find a, b 2 R so that Y = aX + b has expected value 0 and variance 1. (ii) Let X1,X2, . . . independent random variables with Bernoulli( 1/3 )‐distribution. Let n Sn := Σ Xi. i=1 Find a, b 2 R so that Y = aS20 + b has expected value 0 and variance 1.

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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Question

i) Let X ~Binom(100, 1/4 ). Find a, b 2 R so that Y = aX + b has expected value 0 and variance 1.
(ii) Let X1,X2, . . . independent random variables with Bernoulli( 1/3 )‐distribution. Let

n
Sn := Σ Xi.
i=1

Find a, b 2 R so that Y = aS20 + b has expected value 0 and variance 1.

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