Exercise $7\mathrm{.}27-$ The Birthday Problem

Make a matlab function BirthdayProblem.m with the declaration

function $p=$ BirthdayProblem$(n)$

where n is a number of people and p is a probability vector. You can find the details of the Birthday Problem in the textbook,

but I am making the following modifications to the instructions:

The Birthday Problem primary function will create an $(n-1)-$vector of probabilities and a plot of those probabilities versus $n.$ You

will perform a numerical experiment $($described in the problem's hint$)$ in a subfunction that your primary function calls.

So if I input

$p=$ BirthdayProblem$(40)$

p should be a vector of length $n-1$ that holds the probabilities of $2,3,4,$dots,$40$ people sharing a birthday and your program

should create a plot of these probabilities. Inside your program, each of these individual probabilities should be calculated by

calling a subfunction that runs the numerical experiment for a given value of people. Use a loop call the subfunction to do the

experiment $n-1$ times.