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Chapter 5 and 6 notes Discrete and Continuous Probability Distributions

Discrete Probability Distributions

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Discrete Probability Distribution Learning Objectives • Distinguish between discrete and continuous random variables • Determine the mean and variance of discrete distributions • Identify the type of statistical experiments that can be described by

the binomial or Poisson distribution and know how to calculate probabilities using each of them.

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Calculating the Mean of a Discrete Probability Distribution

Summation symbol. Means compute the overall sum of all the products of outcomes and associated probabilities

The product of outcome (Xi) and the associated probability P(Xi)

Calculating the Standard Deviation of the Discrete Probability Distribution

i i

1) Compute the mean of the discrete probability distribution

2) Square the difference between an outcome (Xi) and the mean

3) Compute the product of #2 with the associated probability for each outcome (Xi)

4) Compute the overall sum of the products calculated in #2 for all outcomes (Xi)

5) Take the square root of the sum computed in #4

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Calculating the Mean, Standard Deviation, and Variance of a

Discrete Probability Distribution in Excel

• Consider creating the following 6 columns table headings in Excel

• Enter the appropriate formulas in the initial row of the table • Use the filler handle to copy the formulas down each column for the

total number of outcome rows

i ii i i (Xi)(Xi)

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Binomial Probability Distribution

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Use the Random Number Generator to generate a binomial distribution data set

Sample Size

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Poisson Probability Distribution

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Continuous Probability Distributions

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Normal Probability Distribution

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Exponential Probability Distribution

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