Multinomial and Hypergeometric Distributions (SOA Exam P – Univariate Random Variables)

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After completing this video you should be able to:

- Explain and calculate expected value and higher moments, mode, median, and percentile.

Example 1: Binomial Distribution

An urn contains 25 red balls and 15 black balls. A ball is randomly selected from the urn, its color recorded, and then it’s returned to the urn. This process is repeated 12 times. Let 𝑁_𝑅 denote the random variable representing the number of red balls recorded. Determine 𝐸[𝑁_𝑅] and 𝑉𝑎𝑟(𝑁_𝑅 ).

There are 12 independent trials. Each trial ends in one of two outcomes, either a success or failure.

Example 2: Multinomial Distribution

An urn contains 25 red balls and 15 black balls and 10 green balls. A ball is randomly selected from the urn, its color recorded, and then it’s returned to the urn. This process is repeated 12 times. Let 𝑁_𝑅 denote the random variable representing the number of red balls recorded. Determine 𝐸[𝑁_𝑅] and 𝑉𝑎𝑟(𝑁_𝑅 ).

There are 12 independent trials. Each trial ends in one of three outcomes.

Example 3: Hypergeometric Distribution

An urn contains 25 red balls and 15 black balls. A ball is randomly selected from the urn. The color is recorded, but it is not returned to the urn. This process is repeated 12 times. Let 𝑁_𝑅 denote the random variable representing the number of red balls recorded.

There are 12 dependent trials, with each trial ending in either a success or failure.

0:00 Introduction
1:11 Example 1
2:22 Binomial Distribution
6:01 Example 2
6:39 Multinomial Distribution
12:33 Example 3
14:56 Hypergeometric Distribution
20:37 Example 4