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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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]?

Expert Solution
Given

X : voltage of a noisy resistor 

 

Therefore, 

X ~ N(mean :μ = 0, standard deviation :σ = 2 = 1.414213562)

 

Also, Y=X+2

 

To find:

P[Y>2]

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