A Note on the Probability of Winning a Lottery when the Number of Competitors is a Binomial Random Variable
AbstractConsider a model in which a consumer faces a lottery with j other people for a prize, so that the probability of winning the prize is 1/(j+1). Now let j be a random variable, determined by the binomial distribution. Specifically, let there be n potential competitors for the consumer in the lottery, each with an independent probability of ? of being a competitor. In this note, we show how the resulting expression for the expected value of 1/(j+1) using binomial probabilities can be simplified by means of the binomial theorem.
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Bibliographic InfoPaper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/48.
Length: 4 pages
Date of creation: 11 Aug 2010
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Binomial Distribution; Binomial Theorem; Lottery;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
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