Problem $2$: Covariance

Given a dataset with two variables sampled from a population.

X:$1,2,3,4,5$

$Y$:$2,3,5,7,11$

a$.$ Calculate the sample mean of X and $Y.$ Show your work.

b$.$ Calculate the sample covariance between X and $Y.$ Show your work.

c$.$ Recompute the mean of X and $Y,$ and sample covariance using Python, performing this task in two distinct ways:

$($i$)$ Manually code the sample mean, and sample covariance formulas to calculate these statistics. Ensure your code accurately reflects

the mathematical definitions of these measures.

$($iI$)$Utilize Python's built$-$in functions or relevant libraries $($e$.$g$.,$ NumPy$)$ to compute the sample mean of X and $Y$ and sample covariance.