School

Western University
Department

Economics

Course Code

Economics 2150A/B

Professor

Kristin Denniston

Economics 2151B

Monday March 12

Lecture 17

Chapter 15 â€“ Uncertainty and Imperfect Information

Homework 4

â€¢Due Monday March 24

â€¢Chapters 14 and 15

â€¢Under â€˜Tests and Quizzesâ€™ on OWL

Describing Risky Outcomes

Random Event: An event that has several possible outcomes, each of which is

uncertain

â€¢Each outcome occurs with some probability

â€¢eg. rolling a die (there are 6 possible outcomes, each with a 1/6 chance of being

rolled)

â€¢If you have listed all of the possible outcomes, their occurrence will sum to 1

o1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1

We can create a Probability Distribution for the random event.

â€¢A probability distribution tells us all of the possible outcomes that could occur,

and their associated probabilities of occurrence.

Example: A stock price is currently $100. There is a 30% chance that the stock price

increases to $120, a 40% chance that the stock price stays the same, and a 30%

chance that the stock price decreases to $80.

â€¢We can create a probability distribution from this information.

oThere are only 3 possible outcomes, and they all have their own

probability of occurrence (which will sum to 1)

â€¢You can view the graph in Figure 15.2 (page 1 of your notes)

We describe a random event using:

1. Expected Value

â€¢E(x) =

âˆ‘xP(x)

2. Variance

â€¢Describes the spread in outcomes

â€¢Variance represents riskiness â€“ the higher the variance, the higher the

uncertainty of your outcomes

â€¢

âˆ‘.

x

[x â€“ E(s)]2P(x)

â€¢Example from above stock price: v(x) = (80-100)2(.3) + (100 â€“ 100)2(.4) +

(120 â€“ 100)2(.3) = 240

3. Standard Deviation =

âˆš

variance

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