Question

A book page contains on average 50 lines and each line contains on average 60 characters. The probability that there is character typo is 0.0001. A line or a page contains a random amount of character typos and we want to use the laws or probability to study them. We designate by X, the random variable related to the number of character typos in a line and Y is the random variable related to the number of character typos in a page.

1) Determine the laws of probability of the random variables X and Y

2) Calculate the probabilities of finding in 1 line- 0 typos, 1 typos, 2 typos, at least 1 typo

3) Calculate the probabilities of finding in 1 page- 0 typos, 1 typos, 2 typos, at least 1 typo

4) Calculate the probabilities of finding 2 typos in a page, and the two typos being on the same line

Answer 1

1)

When we want to predict the probability of certain events in a fixed interval of time and we know the average occurrence of that event, Poisson distribution follows. The probability mass function of Poisson distribution is,

The random variable X and Y follows the Poisson distribution with parameter lambda (the mean value)

For random variable, X

For random variable, Y

2)

For 0 typos,

For 1 typo,

For 2 typos,

For at least 1 typo,

3)

For 0 typos,

For 1 typo,

For 2 typos,

For at least 1 typo,

4)

Using the conditional probability law,

Since character typo in a line or in a page are independent events,