Suppose you are analyzing the performance of a randomized QuickSort algorithm on an array of $\backslash ($ n $\backslash )$ elements. You know that the expected number of comparisons made by randomized QuickSort is $\backslash ($ O$($n $\backslash$log n$)\backslash ).$ However, you are interested in the probability distribution of the actual number of comparisons.$($a$)$ How would you model the number of comparisons as a random variable?$($b$)$ What would you expect the variance of this random variable to be$?($c$)$ If you run the randomized QuickSort on an array of $100$ elements, what is the probability that it will make more than $1,000$ comparisons?Would you like to delve into how we might approach solving part $($a$),($b$),$ or $($c$)?$ Let me know which part interests you, and we can explore it further.