Write a python program.

Generate $20,000$ random numbers, each of which is a sum of X and Y$.$ X follows a log$-$normal distribution with parameters $\backslash$mu $=0\mathrm{.}2$ and $\backslash$sigma $=0\mathrm{.}5$; Y follows a normal distribution with $\backslash$mu $=0\mathrm{.}2$ and $\backslash$sigma $=0\mathrm{.}5.$ Once random numbers are generated, compute the mean and variance.

Repeat this process for $1000$ times and record all results in an array. Save only the first $10$ rows and the last $5$ rows to a text file.

You are required to complete this task using TWO approaches: $($a$)$ without for$-$loops and $($b$)$ with for$-$loops. Name those two files as $$task$2$outputHW$6\_$a$.$txt$$ and $$task$2$outputHW$6\_$b$.$txt$,$ respectively. Add a screenshot $($see below for a sample$)$ to your notebook indicating that output text file is generated.

Additional: $($compare the computational efficiencies of two approaches.$)$