1. © 2001 Prentice-Hall, Inc.Chap 5-1 BA 201 Lecture 7 The Probability Distribution for a Discrete Random Variable

2. © 2001 Prentice-Hall, Inc. Chap 5-2 Topics The Probability of a Discrete Random Variable

3. © 2001 Prentice-Hall, Inc. Chap 5-3 Population and Sample PopulationSample Use parameters to summarize features Use statistics to summarize features Inference on the population from the sample p.??

4. © 2001 Prentice-Hall, Inc. Chap 5-4 Types of Data p.9

5. © 2001 Prentice-Hall, Inc. Chap 5-5 Random Variable Outcomes of an experiment expressed numerically E.g. Toss a die twice; count the number of times the number 4 appears (0, 1 or 2 times) E.g. Toss a coin; assign $10 to head and -$30 to a tail = $10 T = -$30

6. © 2001 Prentice-Hall, Inc. Chap 5-6 Discrete Random Variable Obtained by Counting (1, 2, 3, etc.) Usually a finite number of different values E.g. Toss a coin 5 times; count the number of tails (0, 1, 2, 3, 4, or 5 times)

7. © 2001 Prentice-Hall, Inc. Chap 5-7 Probability Distribution Values Probability 01/4 =.25 12/4 =.50 21/4 =.25 Discrete Probability Distribution Example Event: Toss 2 Coins. Count # Tails. T T TT This is using the A Priori Classical Probability approach.

8. © 2001 Prentice-Hall, Inc. Chap 5-8 Discrete Probability Distribution List of All Possible [X j, P(X j ) ] Pairs X j = Value of random variable P(X j ) = Probability associated with value Mutually Exclusive (Nothing in Common) Collective Exhaustive (Nothing Left Out)

9. © 2001 Prentice-Hall, Inc. Chap 5-9 Summary Measures Expected value (The Mean) Weighted average of the probability distribution E.g. Toss 2 coins, count the number of tails, compute expected value

10. © 2001 Prentice-Hall, Inc. Chap 5-10 Summary Measures Variance Weight average squared deviation about the mean E.g. Toss 2 coins, count number of tails, compute variance (continued)

11. © 2001 Prentice-Hall, Inc. Chap 5-11 Computing the Mean for Investment Returns Return per $1,000 for two types of investments P(X i Y i ) Economic condition Dow Jones fund X Growth Stock Y.2 Recession-$100 -$200.5 Stable Economy+ 100 + 50.3 Expanding Economy + 250 + 350 Investment

12. © 2001 Prentice-Hall, Inc. Chap 5-12 Computing the Variance for Investment Returns P(X i Y i ) Economic condition Dow Jones fund X Growth Stock Y.2 Recession-$100 -$200.5 Stable Economy+ 100 + 50.3 Expanding Economy + 250 + 350 Investment

13. © 2001 Prentice-Hall, Inc. Chap 5-13 Computing the Coefficient of Variation for Investment Returns Investment X appears to have a lower risk (variation) per unit of average payoff (return) than investment Y Investment X appears to have a higher average payoff (return) per unit of variation (risk) than investment Y p.183

14. © 2001 Prentice-Hall, Inc. Chap 5-14 Doing It in PHStat PHStat | Probability Distributions | Covariance and Portfolio Analysis Fill in the probabilities and outcomes for investment X and Y Manually compute the CV using the formula Here is the Excel spreadsheet that contains the results of the previous investment example. pp.246-247

15. © 2001 Prentice-Hall, Inc. Chap 5-15 Summary Addressed the Probability of a Discrete Random Variable