6. From the document "American Housing Survey for the United States", published by the U.S. Census Bureau, we obtained the following frequency distribution for the number of persons per occupied housing unit, where we have used "7" in place of "7 or more." Frequencies are in millions of housing units. (13 marks: 2 marks for a. and b., 4 marks for c. and 5 marks for d.) Persons 1 2 3 4 5 6 7 Frequency 27.9 34.4 17.0 15.5 6.8 2.3 1.4 For a randomly selected housing unit, let Y denote the number of persons living in that unit. a. Determine the probability distribution of Y. b. Construct a probability histogram for Y. c. Find and interpret the mean of the random variable. d. Obtain the standard deviation of the random variable.