# Lecture Assignments - Summer 2017

**Assignment # 1: Hand Simulation**.

Point: 100

Due Date: 5:00pm Friday July 14, 2017

**Assignment # 2: Generating Random Numbers - 1**.

Point: 100

Due Date: Wednesday July 19th, 12:50pm

**Problem 1**: Generate all possible random numbers by the LCG (93, 7, c, X_{0}). For X_{0} use the
day number of you birthday. For c value, add the digits of your birth year.You can use Excel for calculations and copy it into your report,
but you must explain what the numbers are and how they are calculated. Identify the period of LCG and if it is not a full period
identify the random numbers that are missing. Use only three digits of decimals. Find U_{437} for this LCG without using Excel.

**Problem 2**:
An experiment involves throwing a die three times and recording the total number of dots observed. Generate
8 random numbers simulating this experiment using the first 8 random numbers generated in problem 1.

**Problem 3**: Add all digits of your phone number. Now, divide it by 3. Use that as a decimal value between 0 and 1 to
represent the probability of success in a Bernoulli experiment. For example, a phone number of 443-885-3235
will be 4+4+3+8+8+5+3+2+3+5 = 45 and third of it will be 15 making p=0.15. Use Excel to generate 100 Bernoulli (p) and 100
Geo (p) using your RV-bank beginning from a cell that has closest value to 0.5 and moving column-wise. Use the generated Bernouli values
to generate 8 values from Bin (7, p). Use the generated Geometric values to generate 8 values from NegBin (7, p).

**Problem 4**: Generate two values from Poi (6.nn) where nn is the total values of phone number digits you calculated in Problem 3.
Use RV-bank beginning with the last value, going row-wise.

**Problem 5**: Generate four values from LogNor (n, 2.25). Where n is the largest digit of Student ID.
Use RV-bank beginning with the closest value to 0.66, going column-wise.

**Assignment # 3: Generating Random Numbers - 2**.

Point: 60

Due Date: Friday July 21st, 4:00pm

**Problem 1**: Use Microsft Excel for steps 1, 2 and 3.

1. Use Data Analysis Add-ins tool to generate 2600 random variables distributed as Poisson with parameter λ. Parameter λ
is in the form of N.nn where N is the largest digit of your student ID and nn is the day number of you birthday. The generated values must be
in 100 rows (rows 1 through 100) and 26 columns (column A through Z). They must be with three decimal values.

2. For each row calculate the average of the values in that row (in column AA).

3. Use these values in ARENA to find the distribution that is the best fit and report it. If that distribution is Normal, go to the next step,
otherwise fit a normal distribution to the data and go to the next step.

4. Use the Normal distribution that you came up with and analytically find the Pr(μ- 2 σ ≤ x ≤ μ + 2σ).Now count the actual
number of averages that fall into that range. Are they very close or not?

**Problem 2**: Use your RV-Bank beginning from random number in row 8, column 8 and moving columnwise. Generate one
random number from a gamma distribution where β = 2nd largest number in your cell phone number and α = 0.length of your longest finger in millimeters.

**Problem 3**: Use your RV-Bank beginning from random number in row 4, column 4 and moving rowwise. Generate one
random number from a gamma distribution where β = 2nd largest number in your student ID number and α = month of your birth.length of
your shortest finger in millimeters.

# Archive Assignments - Spring 2017

**Assignment # 1: Hand Simulation**.

Point: 100

Due Date: Tuesday January 31st, 5:00pm

**Assignment # 2: Generating Random Numbers - 1**.

Point: 100

Due Date: Friday February 3rd, 5:00pm

**Problem 1**: Generate all possible random numbers by the LCG (97, 7, 11, X_{0}). For X_{0} use your the
day number of you birthday. You can use Excel for calculations and copy it into your report, but you must explain
what the numbers are and how they are calculated. Identify the period of LCG and if it is not a full period
identify the random numbers that are missing. Use only three digits of decimals. What is U_{831} for this LCG?

**Problem 2**:
An experiment involves throwing a die twice and recording the total number of dots observed. Generate 5 random numbers simulating this
experiment using the first 5 random numbers generated in problem 1.

**Problem 3**:
Launch Excel. on A1 cell enter *=RAND()*.

A random number between 0 and 1 will appear. Click on that number and drag the handle at the lower corner
of the highlighted box to the right for 20 columns, then down for 20 rows. You should now have 400 random
values all between 0 and 1.

Note: These numbers are dynamic and will change with any action take on the sheet. For example, move the cursor
to a blank cell and press *Delete* few times and watch how the values change with every *Delete* pressing.
The reason is that every cell is represented by the function RAND() which when invoked will generate a new value.
We need to fix the values.

Highlight (select) all 400 cells again and right-click inside the box and select *Format Cells ...*. On the
ensuing window select *Number* tab, *Number* option and change *Decimal place* to 4
and click *OK*.

While still the whole set is selected, click on *Copy* icon from Home tab of Excel ribbon (or, just simply
use *Ctrl+C* from keyboard.)

Launch Notepad and use Edit, Paste (or Ctrl+V) to paste the values into the Notepad.

Block all values and copy them. Go to back to Excel and paste the clipboard onto Excel over the same values (which still be highlited).

Change Sheet1 name to My RV Bank.

Save you Excel file using standard file saving guidelines and email it to the instructor
and inclue a copy in your report. Identify (color) the larges, smallest values in the table and the cell that has closest value to 0.5.

**Assignment # 3: Generating Random Numbers - 2**.

Point: 70

Due Date: Tuesday February 7th, 5:00pm

**General Instruction**: When you are instructed to use your RV-bank starting from a cell (i, j) row-wise, here is
what you need to do:

1. Pick the value at row i and column j of your RV-bank as your first number.

2. Move to cell (i, j+1) and pick that number as your second number.

3. Continue until you reach the last value on row i.

4. If you need more numbers continue to the next row (i+1).

5. If you happened to be at the last row (row 20) and need more numbers go to row 1.

6. Similar approch is used for column-wise selection but instead of the next number being (i, j+1) it will be (i+1, j).

**Problem 1**: Add all digits of your phone number and then divide it by 2. Use that as a decimal value between 0 and 1 to
represent the probability of success in a Bernoulli experiment. For example, my phone number of 443-885-3135
will be 4+4+3+8+8+5+3+1+3+5 = 44 and half of it will be 22 making p=0.22. Use Excel to generate 100 Bernoulli (p) and 100
Geo (p) using your RV-bank beginning from a cell that has closest value to 0.5 and moving column-wise. Use the generated Bernouli values
to generate 10 values from Bin (10, p). Use the generated Geometric values to generate 10 values from NegBin (10, p).

**Problem 2**: Generate two values from Poi (5.nn) where nn is the total values of phone number digits you calculated in Problem 1.
Use RV-bank beginning with the first value, going row-wise.

**Problem 3**: Generate four values from LogNor (n, 1.69). Where n is the largest digit of Student ID.
Use RV-bank beginning with the first value, going column-wise.

**Assignment # 4: RV Maze**.

Point: 70

Due Date: Monday February 13, 5:00pm

**Assignment # 5: Generating Random Numbers - 3**.

Point: 60

Due Date: Wednesday February 15th, 5:00pm

**Problem 1**: Use your all 400 values from your RV-bank. If your birth month
is in January through June, then select row-wise,
otherwise, column-wise. Generat 400 random numbers from TRIA (4.63, 7.05, 13.94) using the formula in the handout.

**Problem 2**: Use your all 400 values from your RV-bank. If your birth month
is in January through June, then select column-wise,
otherwise, row-wise. Generat 400 random numbers from TRIA (4.63, 7.05, 13.94) using the
Acceptance-Rejection method. (Note that you may need to generate
more random numbers from U(0,1)because some of the numbers from your
RV-bank may be rejected). See solution [Link]

**Problem 3**: Use ARENA
Input Analyzer to identify the best distribution fit to the data in problems 1 and 2 and compare.
If there are any differences, research to find out why such differences migh exist.

**Bonus Problem** 20 points: University has Matlab, SPSS, and Maple licensed software on most computer labs. Research and
find out how you can use one of those software to fit a distribution to your two datsets. Is the answer different than the ones you found in
in Problem 3?

**Assignment # 6: Generating Random Numbers -4 & Queuing- 1**.

Point: 60

Due Date: Before Monday February 27th, 9:00am

**Problem 1**: Use your your RV-bank starting at (7, 14) row-wise.
Generat 5 random numbers from UNIF (4.33, 4.85) using the accepatnce-rejection method with a
Triangular majorizing function with a = 2.78 and m = 4.62. (20
points)

**Problems 2-5**: Solve problems 1-4, Chapter 2 of
your textbook (40 points)

**Bonus Problem** 20 points: Problem12 of same
Chapter.