M|M|1 queue

I have an assignment to solve. Questions are as below:

(a) Write a computer program that simulates the number of customers in a M/M/1 queue.

(b) Based on this program plot probability of n customers against n when λ= 4 and µ = 5.

(c) Again, from your program, find the expected number and expected delay in your M/M/1 queueing system when ƿ=1/2.

For part-a will this formula work (Average no. of customers = λ/(λ-µ). But no input given for arrival and service rate?

For part-b we have the formula = ƿ^n*(1-ƿ). Can I generate n randomly or I have to values generated by part-a.

If part-a,b solved then part-c is plug in formula.

Looking for your inputs.