A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and variance equal to 2. The voltage X is linearly transformed through the relation Y=X+2 to obtain the new voltage Y. What is the probability P[Y>2]?

A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and variance equal to 2. The voltage X is linearly transformed through the relation Y=X+2 to obtain the new voltage Y. What is the probability P[Y>2]?

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

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A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean
and variance equal to 2. The voltage X is linearly transformed through the relation Y=X+2 to
obtain the new voltage Y. What is the probability P[Y>2]?

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Expert Solution

Given

X : voltage of a noisy resistor

Therefore,

$X ~ N (m e a n : μ = 0, s \tan d a r d d e v i a t i o n : σ = \sqrt{2} = 1.414213562)$

Also, Y=X+2

To find:

P[Y>2]

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