An economist wants to estimate the average number of cars per household in the country. Suppose that the actual data is as follows: 20% of the households do not have a car, 50% of the households have 1 car, 20% of the households have 2 cars, 10% of the households have 3 cars. For simplicity, the economist assumes in his model that no households have more than 3 cars.
The economist plans to use the following procedure: randomly select 100 households and record the number of cars owned by each of them. Then take the average of these 100 numbers as an estimate of the required average number of cars per household.
Suppose the economist obtains the following data: among 100 randomly selected households, 25 do not have a car, 52 have one car, 15 have 2 cars, and 8 have 3 car».
What is the population distribution in this problem? The values of random variables are discrete (so it can’t be Normal), the graph of the distribution is bell-shaped. It is definitely not Bernoulli, Binomial or Geometric. Could it be Poisson?