- #1
cse63146
- 452
- 0
Homework Statement
Suppose a person's score X on a math aptitude test is a number between 0 and 1, and their score Y on a music aptitude test is also between 0 and 1. Suppose further that in the population of all college students in Canada, the scores X and Y are distributed according to the joint probability density function
[tex]f(x,y) = \frac{2}{5}(2x + 3y) if 0 \leq x \leq 1 and 0 \leq y \leq 1[/tex]
0 otherwise.
a) What proportion of college students obtain a score greater than 0.8 on their math test?
b) If a randomly selected student's score on the music test is 0.3, what is the probability that this student's score on the math test will be greater than 0.8?
Homework Equations
The Attempt at a Solution
a)
[tex]P (X > 0.8) = \int^1_0 \int^1_{0.8} \frac{2}{5}(2x + 3y) dx dy [/tex]
b)
[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} \rightarrow P (X > 0.8 | Y = 0.3) = \frac{P((X>0.8)\cap(Y=0.3))}{P(Y = 0.3)}= \frac{\int^1_{0.8} \frac{2}{5}(2x + 3(1)) dx }{0.3}[/tex]
Did I set up both questions correctly?