Expectation value for first success in a binomial distribution?

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SUMMARY

The expected number of trials to achieve the first success in a binomial distribution with success probability p is calculated as 1/p. This conclusion is derived from the properties of the geometric distribution, which models the number of trials until the first success occurs. The discussion emphasizes that this is not a homework problem but rather a curiosity about statistical principles. For practical applications, understanding this concept can aid in various fields that utilize binomial distributions.

PREREQUISITES
  • Understanding of binomial probability distributions
  • Familiarity with the concept of expected value
  • Basic knowledge of geometric distributions
  • Statistical sampling techniques
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  • Study the properties of geometric distributions in detail
  • Learn about the derivation of expected values in probability theory
  • Explore applications of binomial distributions in real-world scenarios
  • Investigate the relationship between binomial and geometric distributions
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Statisticians, data analysts, students of probability theory, and anyone interested in understanding the implications of binomial distributions in practical applications.

pellman
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This is not a homework problem. Just a curiosity. But my statistics is way rusty.

Suppose a binomial probability distribution with probability p for a success. What is the expected number of trials one would have to make to get your first success? In practice, this means if we took a large number of samples where we stopped at the first success and wrote down the number of trials N to get that success, what is the mean value of N?
 
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