Applicants for the University of Statland take two tests, one for writing ability and the other on critical thinking, and normalized scores are recorded on each between 0 and 1. For a given applicant, let X be the score on the writing test and YY the score on the critical thinking test. A model for the joint probability density function for the two test scores can be taken as:

f(x, y) = { x+y for 0 < x < 1, 0 < y < 1

{ 0 elsewhere.

(a) Find the marginal density of the writing test score, and evaluate it at the point X = 1/2.

(b) Find the marginal density of the critical thinking test score, and evaluate it at the point Y = 1/3.

Two groups of students were asked how many hours they spent reading each day. the table below shows the numbers for each group: group a 1 2 1 1 3 3 2 2 3 group b 3 2 3 2 2 2 1 1 2 based on the table, which of the following is true? the interquartile range for group a students is 0.5 less than the interquartile range for group b students. the interquartile range for group a students is equal to the interquartile range for group b students. the interquartile range for group a employees is 0.5 more than to the interquartile range for group b students. the interquartile range for group a employees is 1 more than the interquartile range for group b students.