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Suppose that the number of typographical errors on a single page of a certain book has a Poisson distribution with parameter λ = 1/2. In 600 pages book, the average number of errors in the book is
  • a)
    300
  • b)
    150
  • c)
    600
  • d)
    393
Correct answer is option 'A'. Can you explain this answer?
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Mean or average of poisson distribution equals its parameter λ
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Calculation of Average Number of Errors

To calculate the average number of errors in a 600-page book, we need to first find the average number of errors on a single page. Given that the number of errors on a single page follows a Poisson distribution with parameter λ = 1/2, we know that the mean of this distribution is equal to λ.

Mean of Poisson Distribution

The mean of a Poisson distribution is equal to its parameter λ. In this case, λ = 1/2. Therefore, the average number of errors on a single page is 1/2.

Calculating Average Number of Errors in the Book

To find the average number of errors in the entire book, we simply multiply the average number of errors on a single page by the total number of pages in the book.

Average number of errors in the book = Average number of errors on a single page * Total number of pages
= 1/2 * 600
= 300

Therefore, the average number of errors in a 600-page book is 300. Option 'A' is the correct answer.
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