Choose the family of distributions that best fits the described situation: You want to model the number of lines of code run until the first 'bug' is detected. The probability a line of code has a bug is 0.003 or 0.3%.

Answer is : Geometric distribution

Let X be the number of lines of codes run until the first bug is detected

That is X is the random variable which is the number of trials needed to get first success. Success here is detection of bug. Success has constant probability in each trail which is p = 0.003. That is before the first success we have X-1 failures with probability (1-0.003)

The probability mass function of X is

P (X=x) = (1-p) x-1 p

P (X=x) = (1-0.003) x-1 * 0.003, x = 1,2, ...

This distribution is also Negative Binomial distribution

As geometric distribution is special case of Negative Binomial Distribution

In Negative Binomial distribution, we have r success (r/geq 1) and the random variable is the number of Bernouli trials needed to get r successes.

If we put, r = 1, that is number of success is 1

Then the given situation, that is number of lines code run (X) before the first bug follow negative binomial distribution

The probability mass function of Negative Binomial distribution is

P (X=x) = (1-p) x-r pr, x = r, r+1, ...

The probability mass function of X is

P (X=x, r=1) = (1-0.003) x-1 * 0.003, x = 1,2, ...