M463 Homework 2
Enrique Areyan
June 19, 2013
1.3.4 Let = cfw_0, 1, 2 be the outcome space in a model for tossing a coin twice and observing the total number of
heads. Then:
a) Yes, the event that the coin does not land head both times is E = cfw_0
b) Yes,

M463 Homework 1
Enrique Areyan
June 18, 2013
Use the formula to find the house percentage in the following cases.
1. A horse has probability 1/35 of winning a race but pays only 30:1 odds.
Solution:
House Percentage: = [1P (A)(rpay +1)]100% = [1
1
31
(30+

M463 Homework 4
Enrique Areyan
June 21, 2013
(1.5) #4 Consider the following events:
T0 = cfw_Transmitter sends 0,
T1 = cfw_Transmitter sends 1,
R0 = cfw_Receiver concludes that a 0 was sent
R1 = cfw_Receiver concludes that a 1 was sent
Assume that P (R0

M463 Extra Credit 1
Enrique Areyan
July 23, 2013
1
Find
!, i.e., the factorial of one-half.
2
Solution: Using the Gamma function we know that for any r R
Z
(r + 1) = r!,
where
et tr dt
(r + 1) =
0
First note an important property of this function, i.e.:

M463 Homework 3
Enrique Areyan
June 20, 2013
(1) A family has two children, of whom the oldest is a girl. What is the probability both children are girls?
Solution:
Let = cfw_(G, B), (G, G), where G denotes
(Older, Younger). Consider the following event: