代写ECE2191 Probability Models in Engineering Tutorial 10: Random Sums and Sequences代做Java语言

日期：2025-11-07 05:57

ECE2191 Probability Models in Engineering

Tutorial 10: Random Sums and Sequences

(problems)

Second semester 2021

1. A bank teller serves customers standing in the queue one by one. Suppose that the service time Xi for customer i has mean E[Xi] = 2 (minutes) and V ar(Xi) = 1. We assume that service times for different bank customers are independent. Let Y be the total time the bank teller spends serving 50 customers. Find P(90 < Y < 110).

2. You want to rent an unfurnished three-bedroom house in Clayton. The mean of monthly rent for a random sample of 60 houses advertised on a certain real estate website is $1000. Assume a population standard deviation of $200. Construct a 95% confidence interval.

3. WHO wishes to survey the number of covid-19 cases from a number of countries. If the population standard deviation is 100, how many countries would be needed in a sample in order for the population mean to be within ±50 cases with 90% confidence?

4. Rick Sanchez has invited 64 guests to a party. His grandson Morty helps to make sand-wiches for the guests. Morty believes that a guest might need 0, 1 or 2 sandwiches with probabilities 14, 12, and 14 respectively. Assume that the number of sandwiches each guest needs is independent from other guests. How many sandwiches should Morty make so that he can be 95% sure that there is no shortage?

5. Let X1, X2, . . . , Xn be IID. Exponential random variables with λ = 1. Let

How large should n be such that