Examples

Let us say you have a 200-page ms. To collect some data, you pick 10% (i.e., 20 pages) at random, read each, and count the total number of independent misprints. For example, let us say you find three. Then your estimate for the average is

k = 3 typos/20 pages = 0.15 typo/page

and the Poisson distribution gives the probability for *n* misprints on one page:

*P _{n}* = (0.15)

We can make a table:

n | P_{n} | in 200 pages |
---|---|---|

0 | 0.861 | (0.861)(200) = 172 pages are expected to have no misprints |

1 | 0.129 | (0.129)(200) = 26 pages are expected to have 1 misprint |

2 | 0.010 | (0.010)(200) = 2 pages are expected to have 2 misprints |

The results tabulated above are only estimates, because your value for k is an estimate. But these estimates are sufficient to help you decide whether you should keep rereading: If you are satisfied with 30 misprints in 200 pages, then you declare victory. Otherwise, you reread and delete more errors.

With an estimate for the average k, we can ask other questions. For example, for the situation in Example 1, what is the probability of there being one misprint on each of two successive pages?

Since the misprints are independent, the probability of these two events is just the product of the probabilities of the two individual events,

*P* = *P _{1} P_{1}*

Using values from Example 1,

*P* = (0.129) × (0.129) = 0.0166

So in 200 pages, we expect there will be (0.0166) × (200) = 3 times when two successive pages each have a misprint.

Extending the idea in Example 2, what is the probability of there being one misprint on a page, if the previous page had no misprint?

*P* = *P _{0} P_{1}*

Using values from Example 1,

*P* = (0.861) × (0.129) = 0.111

So in 200 pages, we expect there will be (0.111) × (200) = 22 times when this occurs. In financial circles, this would be stated as *Past performance is no predictor of future success.*

Distribution of Misprints in Your Manuscript

R. W. Hamming, *The Art of Probability for Scientists and Engineers*, Addison-Wesley, Redwood, CA, 1991.

W. E. Deming, *Some Theory of Sampling*, Dover, New York, 1966; reprint of 1950 edition published by Wiley.