Concept explainers
If Y is a geometric random variable, define Y∗ = Y − 1. If Y is interpreted as the number of the trial on which the first success occurs, then Y∗ can be interpreted as the number of failures before the first success. If Y∗ = Y − 1, P(Y∗ = y) = P(Y − 1 = y) = P(Y = y + 1) for y = 0, 1, 2, …. Show that
The probability distribution of Y∗ is sometimes used by actuaries as a model for the distribution of the number of insurance claims made in a specific time period.
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Mathematical Statistics with Applications
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage