Homework Assignment 4

Purpose: To help you learn about the power that comes with knowing the distribution underlying a data set. We will use this power over and over in this class, mostly to calculate probabilities but sometimes to estimate properties.

You are in the first stages of an analysis of a complex investment opportunity. You don't really know what the annual cash flow will be over the next few years. Your best estimate is that anything in the 1.2 to 3.7 million dollars/year range would be reasonable. Without further information, you assume all results in this range are equally likely. Why? Because when we have no probability information we often just assume the probabilities are equal for all "reasonable" values of the independent variable.

1. What is the name of the distribution you will use?
   Using Excel, make a probability distribution graph. So, x=cash flow and y=probability distribution values (it is called probability density by some authors)? This is a simple graph. You don't need any more data that what is given above. There are several of ways to make this graph, any of which is acceptable. You could use Insert/Picture/AutoShape if you are artistically inclined. Or, you could use a scatter plot. Or you could use a column chart. For the scatter plot, just enter (x, y) points for each corner of the plot. For the column chart, just enter three labels and three f(x) values (two of the "bars" will be of zero height). Whatever method you use, leave some "zero probability" space on both sides of the finite probability range. This helps your reader understand what you are doing. For this assignment, make the x axis run from 0 to 5 million dollars/year.
2. What is the expected value and the standard deviation of x, the random variable in the above scenario? Be sure to show the units on your results and show the equations that you use.
3. What is the average value and standard deviation of your 10,000 data points?
4. Does your answer to Q2 approximately equal your answer to Q3? Why or why not? Explain in detail.

Make a histogram of your 10,000 data points. These points truly are "your" points because no other student will have the same points. Use bins with a width of 0.1 million dollars/year running from 0 to 5 so your x axis will be comparable to your previous graph. You must use the histogram wizard in Excel to make the histogram.

Extra Credit: What if your boss wants you to use a range of x values from 1 to 5 instead of 1.2 to 3.7? Using algebra , what is the ratio of your original standard deviation to the new standard deviation found using the new 1 to 5 range? Show your equation.

Price: $11.58

Solution: The downloadable solution consists of 5 pages, 658 words and 2 charts.
Deliverable: Word Document