Exercise $1.$

Today's lab is a simple plotting exercise, designed to reinforce the idea of Fisher

Information. You will calculate and plot the Fisher information for two normal PDFs

$({}_1,{}_1|)({}_2,{}_2|)=\frac{1}{\sqrt[\phantom{2}]{2}{}_2}{e}^{-\frac{(x-{}_2{)}^2}{2}{}_2^2}$

We will take the widths of these distributions $-{}_1$ and ${}_2-$ to be known, and compute

Fisher information for the parameters ${}_1$ and ${}_2.$

Consider cases in which $f_1$ and $f_2$ have the different means and the same width, e$.$g$.$

${}_1,{}_1=1\mathrm{.}0,0\mathrm{.}3$

${}_2,{}_2=2\mathrm{.}0,0\mathrm{.}3$

and also the case where $f_1$ and $f_2$ have the same means and different widths, e$.$g$.$

${}_1,{}_1=2\mathrm{.}0,0\mathrm{.}3$

${}_2,{}_2=2\mathrm{.}0,0\mathrm{.}6$

Create a Python script $($or Jupyter Notebook$)$ to perform the following:

Generate an appropriately$-$sized $($i$.$e$.$ readable$)5-$panel plot. The horizontal axis

should span $ln(PDF)$