Expected Value- Random variables

1 / 18

# Expected Value- Random variables - PowerPoint PPT Presentation

Expected Value- Random variables. Def. A random variable , X , is a numerical measure of the outcomes of an experiment. Example:. Experiment- Two cards randomly selected Let X be the number of diamonds selected. Events can be described in terms of random variables Example:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Expected Value- Random variables' - Ava

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Expected Value- Random variables

Def. A randomvariable, X, is a numerical measure of the outcomes of an experiment

Example:
• Experiment- Two cards randomly selected

Let X be the number of diamonds selected

Events can be described in terms of random variables

Example:

• is the event that exactly one diamond is selected
• is the event that at most one diamond is selected
In general,

is the probability that X takes on the value x

is the probability that X takes on a value that is less than or equal to x

Def. The mean (or expectedvalue) of X gives the value that we would expect to observe on average in a large number of repetitions of the experiment
Important
• Concept of Expected value describe the expected monetary return of experiment

Sum of the values, weighted by their respected probabilities

Example (Exercise 13):

An investment in Project A will result in a loss of \$26,000 with probability 0.30, break even with probability 0.50, or result in a profit of \$68,000 with probability 0.20. An investment in Project B will result in a loss of \$71,000 with probability 0.20, break even with probability 0.65, or result in a profit of \$143,000 with probability 0.15. Which investment is better?

Tools to calculate E(X)-Project A
• Random Variable (X)- The amount of money received from the investment in Project A
• X can assume only x1 ,x2 ,x3

X= x1 is the event that we have Loss

X= x2 is the event that we are breaking even

X= x3 is the event that we have a Profit

• x1=\$-26,000
• x2=\$0
• x3=\$68,000
• P(X= x1)=0.3
• P(X= x2)= 0.5
• P(X= x3)= 0.2
Tools to calculate E(X)-Project B
• Random Variable (X)- The amount of money received from the investment in Project B
• X can assume only x1 ,x2 ,x3

X= x1 is the event that we have Loss

X= x2 is the event that we are breaking even

X= x3 is the event that we have a Profit

• x1=\$-71,000
• x2=\$0
• x3=\$143,000
• P(X= x1)=0.2
• P(X= x2)= 0.65
• P(X= x3)= 0.15
Focus on the Project
• How can Expected value help us with the decision on whether or not to attempt a loan workout?
• Recall:

Events

S- An attempted workout is a Success

F- An attempted workout is a Failure

Tools to calculate E(X)
• Random Variable (X)- The amount of money Acadia receives from a future loan workout attempt
• X can assume only

Full Value

Default Value

x1=\$ 4,000,000

x2=\$ 250,000

The sheet Expected Value in the Excel file Loan Focus.xls performs the following computation for the expected value of X.

• Using Expected value formula
Decision?

Recall

• Bank Forecloses a loan if

Benefits of Foreclosure > Benefits of Workout

• Bank enters a Loan Workout if

Expected Value Workout > Expected Value Foreclose

Since the expected value of a work out is \$1,991,000 and the “expected value” of foreclosing is a guaranteed \$2,100,000, it might seem that Acadia Bank should foreclose on John Sanders’ loan.