Part $($a$)$: Adding resistors in series

Suppose we have three resistors of type $$ and two resistors of type $,$ all attached in series. The formula for the total resistance $$ is the sum of all resistances:

$=3+2$

Assume that resistors of type A are all identical and with resistance

$=85\backslash$pm $5$ohms.

Likewise resistors of type $$ are all identical with resistance

$=120\backslash$pm $6$ohms.

Your tasks are as follows:

Determine $($and print$)$ the central value and error on $$ following the "usual method" i$.$e$.,$ from Eq$.(1$a$)$ and $(1$b$).$

Next, you will determine the central value and error on $$total using Monte Carlo sampling. Specifically, your tasks are as follows:

Generate $=105$ samples for both $$ and $$ from normal distributions. For sampling $,$ you set $$ and $$ to be the central value and error on $$ quoted above $($and similarly for $).$

Obtain $$ samples for $$ from your samples for $$ and $,$ according to the formula above. That is$,$ for each sample $,,$ you obtain $=3+2$ as a sample for $.$

Calculate and print the mean and standard deviation for $$ from your samples.

Your results from both methods should agree