Calculating Variance of Y using Poisson and Binomial Distributions

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SUMMARY

The variance of Y, representing the number of pages without errors among the first 112 pages, is calculated using both Poisson and Binomial distributions. The Poisson distribution with a lambda of 0.40 provides the probability of a page having no errors, which is then used in the Binomial variance formula. The correct calculation involves using the Poisson probability to determine p, followed by applying the Binomial variance formula: variance = n * p * q, where n equals 112 and q is 1 - p. This method yields the accurate variance for Y.

PREREQUISITES
  • Understanding of Poisson distribution and its properties
  • Familiarity with Binomial distribution and variance calculation
  • Basic knowledge of probability theory
  • Ability to perform calculations involving lambda, n, p, and q
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  • Explore Poisson distribution calculations using statistical software like R or Python
  • Learn about the relationship between Poisson and Binomial distributions
  • Study variance calculations in different probability distributions
  • Practice problems involving mixed distribution scenarios
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Students in statistics, data analysts, and anyone interested in understanding variance calculations using Poisson and Binomial distributions.

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Homework Statement


I need to find the variance of Y.

The number of errors on a page follows a Poisson distribution with lambda = 0.40 average . Y = the number of pages without error among the first 112 pages .

Homework Equations

The Attempt at a Solution


In Poisson, I know that Variance = lambda= 0.40
In Binomial, Variance = n*p*q
1-p = q
Do I simply do 112 x 0.4 x 0.6 to find the variance of Y? How am I supposed to do it?
 
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First use the Poisson to work out the probability of a page having no errors. Then use that number in the Binomial distribution to solve the problem.
 
andrewkirk said:
First use the Poisson to work out the probability of a page having no errors. Then use that number in the Binomial distribution to solve the problem.
I got this resolved by doing

poissPdf(0.4,0) =p
n = 112

variance with binomial = n*p*q
and its correct answer :)
 
Last edited:

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