1. [30 pts.] Data analysis

In a statistical survey of 3000 families on ownership of cars 60 families responded that they do not own a car, 720 families owned 1, 1200 families owned 2, 750 families owned 3, 240 owned 4, and there were 30 families owned 10 cars each.

(a) [5 pts] Plot the sample-based Probability Mass Function (PMF) and Cumulative Distribution Function (CDF) of the random variable corresponding to the number of cars per family.

(b) [5 pts] Calculate the expected the number of cars per family and its variance. Show the steps of your calculation.

(c) [10 pts] Calculate the expected value of number of cars per family if you exclude the families with 10 cars. Is the mean stable or sensitive to the removal of these data points? What other statistical measures are there to estimate the average behavior? Are they less or more stable with regard to the outliers? Justify your answer by computing those alternative measures for the original sample.

(d) [10 pts] Create a box plot for the number of cars per family for the variables X_all (cars per family including all observations) and X_-10 (cars per family after excluding the 10-car families) (don't use python libraries for this - just draw it by hand in your submission). Look here: http://www.physics.csbsju.edu/stats/box2.html for examples of box plots. You should have two boxes one for X_all and one for X_-10 with their specific statistics: mean, median, ranges, and inter-quantile ranges (see slides on numeric attributes for details).