Computer Science Data Sci questions. Sorry that there are many small questions but please help me as many as you can. I will appreciate. I will give an upvote.

No need to type in Latex format, just regular work, thank you!

You are waiting in line at the grocery store. It is taking forever! There are only two lines open; one is being tended by a cashier named John Henry), and the other is tended by a self check-out machine. Like all human beings when they arrive at the front of the store to check-out and encounter lines everywhere, you first experience a moment of intense panic. Which line will be the fastest? you wonder, as people shuffle around you. You decide you need to model the arrival of customers at the front of each of the lines. From your Intro to Data Science class you remember that the distribution of times between independent arrivals is often modeled using an Exponential distribution. You observe the following: John's line checks-out an average of 4 customers per ten minutes, the self check-out machine checks-out an average of 5 customers per ten minutes if the machine is working properly, the self check-out machine checks-out an average of 1 customer per ten minutes if the machine is freezing up, and in any given moment, the self check-out machine has a probability of 0.1 of freezing up Answer the following questions about this scenario. Note that for Parts B-D you should clearly express the computation you're doing with math, but feel free to do any fancy function evaluations with Python. Part A: Assuming the between-customer times do in fact follow exponential distributions, what distributions do you expect the number of customers who pass through each line in a given 10-minute interval to follow? What are the parameter(s) of each distribution? Note that you should consider both the case where the self check-out is working properly and when it is broken. Type Markdown and LaTeX: a Part B: What is the probability that 6 customers pass through John's line in the next 10 minutes? What about the self check-out, assuming that it is working? What about the self check-out, assuming that it is frozen? You are waiting in line at the grocery store. It is taking forever! There are only two lines open; one is being tended by a cashier named John Henry), and the other is tended by a self check-out machine. Like all human beings when they arrive at the front of the store to check-out and encounter lines everywhere, you first experience a moment of intense panic. Which line will be the fastest? you wonder, as people shuffle around you. You decide you need to model the arrival of customers at the front of each of the lines. From your Intro to Data Science class you remember that the distribution of times between independent arrivals is often modeled using an Exponential distribution. You observe the following: John's line checks-out an average of 4 customers per ten minutes, the self check-out machine checks-out an average of 5 customers per ten minutes if the machine is working properly, the self check-out machine checks-out an average of 1 customer per ten minutes if the machine is freezing up, and in any given moment, the self check-out machine has a probability of 0.1 of freezing up Answer the following questions about this scenario. Note that for Parts B-D you should clearly express the computation you're doing with math, but feel free to do any fancy function evaluations with Python. Part A: Assuming the between-customer times do in fact follow exponential distributions, what distributions do you expect the number of customers who pass through each line in a given 10-minute interval to follow? What are the parameter(s) of each distribution? Note that you should consider both the case where the self check-out is working properly and when it is broken. Type Markdown and LaTeX: a Part B: What is the probability that 6 customers pass through John's line in the next 10 minutes? What about the self check-out, assuming that it is working? What about the self check-out, assuming that it is frozen