Some Important Discrete Probability Distributions (PPT)

Basic Business Statistics (8th Edition)
Chapter 5 - Some Important Discrete Probability Distributions

Chapter Topics

• The probability of a discrete random variable
• Covariance and its applications in finance
• Binomial distribution
• Poisson distribution
• Hypergeometric distribution

Random Variable

• 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)

Discrete Random Variable

Discrete Probability
Distribution Example

Discrete Probability Distribution

Summary Measures
Expected value (the mean)
Weighted average of the probability distribution:

Summary Measures
Example of expected value (the mean):
Toss two coins, count the number of tails, compute expected value

Summary Measures

Variance

• Weight average squared deviation about the mean

Summary Measures
Example of variance:
Toss two coins, count number of tails, compute variance

Covariance and its Application
Computing the Mean for Investment Returns
Computing the Variance for Investment Returns

Computing the Covariance
for Investment Returns
Important Discrete

Probability Distributions
Binomial Probability Distribution

• “n” Identical trials
• Two mutually exclusive outcomes on each trial
• Trials are independent

Binomial Probability Distribution

• Constant probability for each trial 
• Two sampling methods

Binomial Probability
Distribution Function
Binomial
Distribution Characteristics

• Mean
• Variance and

Binomial Distribution in PHStat

• PHStat | Probability & Prob. Distributions | Binomial

Poisson Distribution

• Poisson process
• Discrete events in an “interval”
• The probability of success is

Poisson Probability
Distribution Function
Poisson Distribution in PHStat

• PHStat | probability & probability distributions | Poisson

Poisson Distribution Characteristics

• Mean

Hypergeometric Distribution

• “n” Trials in a sample taken from a finite population of size N
• Sample taken without replacement
• Trials are dependent
• Concerned with finding the probability of “X” successes in the sample where there are “A” successes in the population

Chapter Summary

• Addressed the probability of a discrete random variable
• Defined covariance and discussed its application in finance
• Discussed binomial distribution
• Addressed Poisson distribution
• Discussed hypergeometric distribution 

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