A communication system accepts a positive voltage V as input and outputs a volta

Question

A communication system accepts a positive voltage V as input and outputs a voltage Y = alpha V + N. where alpha = 10-2 and N is a Gaussian random variable with parameters m = 0 and sigma = 2. Find the value of V that gives P(Y

Explanation / Answer

Using "normcdf(x)", we determine that for standard Normal (or "Gaussian") variable "Z":      Prob{Z < -4.7534} = 10(-6) Thus, for given Gaussian random variable "N":      Prob{ (N - )/ < -4.7534 } = 10(-6)      ---->    Prob{ (N - (0))/(2) < -4.7534} = 10(-6)      ---->    Prob{N/2 < -4.7534} = 10(-6)      ---->    Prob{N < -9.5068} = 10(-6)      ---->    Prob{ (Y - *V) < -9.5068 } = 10(-6)      ---->    Prob{ (Y - (0.01)*V) < -9.5068 } = 10(-6)      ---->    Prob{ Y < (0.01)*V -9.5068 } = 10(-6)        ---->    Prob{Y < (0)} = 10(-6)                    ---->    (0.01)*V -9.5068 = 0                 ---->    V = (9.5068)/(0.01)                 ---->    V = 950.7 .

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