Question

For each of the following sample spaces, provide the distribution that describes each experiment, and the support of that distribution. Explain why you chose that distribution.

1. X = the number of heads obtained in a series of 100 coin flips.
2. X = the number of months until an appliance breaks.
3. X = the number of cars that go through an intersection during one green light
4. X = the number of hired interns, out of a finite number of applicants, who will be good employees.

Answer 1

In 1st case, It follows a binomial distribution because if we flip the coin either we get head or tail and n=100.

In 2nd case, It follows negative binomial distribution because x is the number of months until an appliance breaks that is no of trials required to get 1st success.

In the 3rd case, It follows Poisson distribution because in the case of Poisson distribution the probability of success is very less.

In the 4th case, It follows the binomial distribution because the intern is either hired on unhired and there is finite no of applications.