Geometric (Negative Binomial) Distributions (SOA Exam P – Probability – 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.

Description: Given a sequence of independent trials such that each trial ends in one of two outcomes, success or failure, let 𝑁 denote the random variable representing the number of failures observed before the 1st success is observed.

𝑁 ~ NB(𝑟,𝑝)
𝑝_𝑘=Pr⁡(𝑁=𝑘)=((𝑘+𝑟−1@𝑘))∙𝑞^𝑘∙𝑝^𝑟
E[𝑁]=𝑟𝑞/𝑝
Var(𝑁) =𝑟𝑞/𝑝^2

Description: Given a sequence of independent trials such that each trial ends in one of two outcomes, success or failure, let 𝑁 denote the random variable representing the number of failures observed before the 1st success is observed.

𝑁 ~ G(𝑝)=NB(𝑟=1,𝑝)
𝑝_𝑘=Pr⁡(𝑁=𝑘)=𝑞^𝑘∙𝑝
E[𝑁]=𝑞/𝑝
Var(𝑁) =𝑞/𝑝^2

Видео Geometric (Negative Binomial) Distributions (SOA Exam P – Probability – Univariate Random Variables) канала AnalystPrep