Using Standardized Gaussian PRNG to Generate Gaussian Noise with Specified $\sigma _ { \mathrm { N } } ^ { 2 }$

question 6

Essay

Using Standardized Gaussian PRNG to generate Gaussian noise with specified variance.The following work sheet specifies the noise variance $\sigma _ { \mathrm { N } } ^ { 2 }$ in A2.Using the standardized Gaussian random numbers generated in Column B form the random noise values having the specified variance in Column C.
a.What is the formula that computes the noise SD in B2?
b.What is the formula in C5?
$$\begin{array} { | c | c | c | c | } \hline & \mathrm { A } & \mathrm { B } & \mathrm { C } \\\hline 1 & \sigma _ { \mathrm { N } } ^ { 2 } = & \sigma _ { \mathrm { N } } = & \\\hline 2 & 4 & 2 & \\\hline 3 & & & \\\hline 4 & \mathrm { i } & \mathrm { G } _ { \mathrm { i } } & \mathrm { N } _ { \mathrm { i } } \\\hline 5 & 0 & - 1.306 & - 2.612 \\\hline 6 & 1 & - 0.734 & - 1.468 \\\hline 7 & 2 & 1.602 & 3.205 \\\hline 8 & 3 & - 1.488 & - 2.975 \\\hline 9 & 4 & - 0.392 & - 0.784 \\\hline\end{array}$$