WeBWorK Standalone Renderer

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

$f \left( x,y \right) = \begin{cases} \frac{2}{3}\left(2x+y\right) & & \text{for } 0<x<1,\text{ } 0<y<1 \\ & & \\ 0 & & \text{elsewhere.} \end{cases}$

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

Part b)
Find the marginal density of the critical thinking test score, and evaluate it at the point $Y=1/4$ .

Part c)
The scores on the two tests are independent.

A. False
B. True

You can earn partial credit on this problem.