Math 362
Final Exam Solutions
Fall 09
1. A certain country has a careless mint. One out of every 801 coins
comes out with two heads. Pick a coin at random and ip it three
times.
a) What is the probability all three tosses are heads? Solution:
101
801
b) W
Math 362
Exam 3 Solutions
Spring 11
1. Consider the density function
10x2 y
0
f (x, y ) =
for 0 x 1, 0 y x,
otherwise.
Compute the following:
a) f1 (x).
b)
c)
d)
e)
f)
g)
x
0
2
10x y dy =
5x2 y 2 |x
0
4
= 5x . f1 (x) =
5x4
0
0x1
otherwise.
1
5
E (X ). 0 5
Math 362
Exam 3 Solutions
Fall 09
1. Consider the density function
for 0 y x 1.
otherwise.
8xy
0
f (x, y ) =
Compute the following:
a) f1 (x). Solution:
x
0
f1 (x) =
8xy dy = 4xy 2 |x = 4x3
0
0 x 1,
otherwise.
0
b) f2 (y ). Solution:
1
y
8xy dx = 4x2 y |1
Math 362
Exam 2
Spring 11
1. Consider the density function
8xy
0
f (x, y ) =
for 0 x 1, 0 y x
otherwise.
a) What is the marginal density function f1 (x)? Solution:
x
0
f1 (x) =
8xy dy = 4x3
0
0x1
otherwise.
b) What are E (X ) and V (X )? Solution:
1
4
x 4
Math 362
Exam 2 Solutions
Fall 09
1. Consider the density function
f (x, y ) =
15x2 y
0
for 0 x 1, x y 1
otherwise.
a) What is the marginal density function f2 (y )?
Solution: The active region is
(0,1)
(0,0)
(1,1)
We have
y
0
f2 (y ) =
15x2 y dx if y
Math 362
Exam 1 Solutions
Spring 11
1. Urn A contains 7 red balls and 3 green balls. Urn B contains
4 red balls and 6 green balls. An experiment is conducted as
follows:
Flip 3 coins. If you get exactly two heads, draw with
replacement from Urn A until yo
Math 362
Exam 1 solutions
Fall 09
1. Urn A contains 7 red balls and 3 green balls. Urn B contains 4 red
balls and 6 green balls. An experiment is conducted as follows:
Roll a pair of dice. If the sum is 5 draw three balls from
Urn A without replacement. O