This preview shows pages 1–3. Sign up to view the full content.
STAT/MA 416
September 21, 2011
Problem Set 13
Name:
1. Winnings and Losing.
Suppose that a person wins a game of chance with probability
0
.
40, and loses otherwise. If he wins, he earns 5 dollars, and if he loses, then he loses 4
dollars.
(a.) What is his expected gain or loss?
(b.) What is the variance of his gain or loss?
(c.) Find constants
a,b
such that if
X
= 0 when he loses and
X
= 1 when he wins, then
Y
=
aX
+
b
is his earnings. [Hint: solve 5 =
a
(1) +
b
and

4 =
a
(0) +
b
. Also:
X
is a
Bernoulli.] Verify your results above by ﬁnding
E
(
Y
) and Var(
Y
) with this method.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 2. Telemarketers.
One out of every eight calls to your house is a telemarketer. You will
record whether the next call is a telemarketer.
(a.) What is the probability that the next time the phone rings, it will be a telemarketer?
(b.) If the phone calls are independent, what is the probability the 3rd call after dinner
will be a telemarketer?
(c.) If you lose 30 seconds of your time every time you have to talk to a telemarketer,
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/28/2012 for the course STAT 416 taught by Professor Staff during the Fall '08 term at Purdue University.
 Fall '08
 Staff
 Probability

Click to edit the document details