Question

Fifteen percent of houses in your area have finished basements. Your real estate agent starts showing you homes at random, one after the other. Let X be the number of homes with finished basements that you see, before the first house that has no finished basement. What is the distribution of X ? If it has a special name, give it (along with any parameters). Also, give its proof.

Answer 1

The distribution of X, the number of homes with finished basements that you see before the first house that has no finished basement, follows a geometric distribution with a probability of success of 0.15. The formula for finding the probability associated with the geometric distribution is P(X = k) = (1-p)^(k-1) * p.

Step-by-step explanation:

The distribution of X, the number of homes with finished basements that you see before the first house that has no finished basement, follows a geometric distribution.

The geometric distribution models the number of trials it takes to achieve the first success in a series of independent

Bernoulli trials (a trial with two possible outcomes, success or failure) with a specific probability of success.

In this case, the probability of success is 15% (0.15), representing the probability of seeing a home with a finished basement.

The distribution of X is denoted as X ~ Geo(0.15).

To find the probability associated with the geometric distribution, we can use the formula:

P(X = k) = (1-p)^(k-1) * p

where P(X = k) represents the probability of seeing k homes with finished basements before the first house without a finished basement, and p represents the probability of success (0.15 in this case).