Show me the steps to solve Exercise $2($Gaussian Distribution$)$ Coding

Use python or R$,$ for creating functions $($or methods$)$ to calculate the Gaussian

Distribution for random data $($x$)$ that is generated by the following f$($x$).$

f$($x$)=12+$ cosine$($x $2)80$

x$=$ f$($x$)$

$(8)$

In your source code, you should:

$1.$ generate random seeds for the variable x to be in the range of $0$ and $1$

$($Hint: you might use linspace from np package in python$),$ the size of

the seeds can be defined in the function$$s argument $($could be any value

$>1).$

$2.$ use $(8)$ to generate $$x using the random seeds x obtained from requirement

$1$ above.

$3.$ transfer the $$x into a normal distribution using the Gaussian distribution

formula $(9)$:

p$($x$)=$ N $($x$|,\backslash$sigma $2$

$)=1$

$\backslash$sigma

$$

$2\backslash$pi

exp$($x$)$

$2$

$/2\backslash$sigma

$2$

$(9)$

$4.$ plot the normal distribution using $$x in the X axis and Gaussian distribution results in the Y axis. $($Hint: for creating a smooth curve, you may

consider using make interp spline from Scipy package in python. Also,

before plotting the normal distribution, sort x$$ for a nice chart!$)$