excel - probabilities ( i need it after 3 hours )

IE 151: Computational Methods in Industrial Engineering

Homework 3

Due: Thursday, March 21st at 11:59 p.m.

Before start, please read the following. 1. You should submit your homework through Canvas by Thursday, March 21st

11:59 pm. Note that the due date/time remains unchanged in any case.

2. In answering the solutions, you must submit your document along with

EXCEL files indicating that you have actually implemented the commands in

EXCEL. (i.e., electronic submissions must have snapshots of all commands in

EXCEL.)

3. You are responsible to send the correct file. If your file is corrupted or not

opened, you will get ZERO.

4. For this homework, late submissions are allowed. The late submission due

is Friday, March 22nd with 30% penalty.

5. You are allowed to share ideas with other students in the class, but your

submission must reflect your own effort in solving the questions. Cheating,

if proved, is subject to cheating policy stated in the course syllabus.

Good Luck! 

Question 1 (10+10 = 20 points)

An Internet service provider company has installed a modem to serve the needs of 1 customer

in an arbitrary region. Suppose that once a connection service is requested by a customer, one

unassigned modem must be immediately assigned to the customer or the request will be denied.

At each time period, a customer may request for a connection service with a probability of 0.7.

a. What is the probability distribution of a customer request for a connection? It suffices to

write the exact formula.

b. Use Excel to generate 10 random numbers for customer requests with Bernoulli

distribution with parameter p = 0.65 (please also add the screenshot of Excel in your

answer sheet)

Question 2 (10+10 = 20 points)

Consider the following system with 15 identical components. As you may guess, this system is

functional provided that every single component is working. Hence, once one of the component

is broken, the system stops working. Each of the components is assumed to independently work

with a probability of 0.8 over a day.

a. What is the probability that this system works the whole day?

b. Now use Excel to compute the probability formula that you provided to part (a).

Question 3 (6++6+6+6+6 = 30 points)

Two dices are rolled at the same time and the squared difference between their top faces is

reported.

a. What is the probability that the squared difference of the top faces is 0?

b. What is the probability that the squared difference of the top faces is 1?

c. In general, how can we calculate the probabilities for all possible values of the squared

difference of the top faces in Excel?

d. Compute the Cumulative Empirical Distribution (CDF) for part c.

e. Plot column charts for both probability (PDF) and CDF.

Question 4 (5+5+5+5 = 20 points)

For each of the parts (a) through (d), write a syntax in Excel.

a. Generate a real number in the range [0,15].

b. Generate a real number in the range [11,19]

c. Generate an integer number in the inclusive range from 1 to 10

d. Generate a fractional number with its integer nominator extracted randomly in the

inclusive range 1 to 2 and its integer denominator extracted randomly in the inclusive

range 1 to 4

Question 5 (10 points)

Using Excel calculate the matrix multiplication. (Hint: use MMULT(array1,array2))