IEOR 3658
Assignment #5
Probability
October 12, 2011
Prof. Mariana OlveraCravioto
Page 1 of 2
Assignment #5
– due October 19th, 2010
1. (From text) A stock market trader buys 100 shares of stock A and 200 shares of stock B.
Let
X
and
Y
be the price changes of A and B, respectively, over a certain time period, and
assume that the joint PMF of
X
and
Y
is uniform over the set of integers
x
and
y
satisfying

2
≤
x
≤
4
,

1
≤
y

x
≤
1
.
(a) Find the marginal PMFs and the means of
X
and
Y
.
(b) Find the mean of the trader’s proﬁt.
2. (From text) A class of
n
students takes a test consisting of
m
questions. Suppose that student
i
submitted answers to the ﬁrst
m
i
questions.
(a) The grader randomly picks one answer, call it (
I,J
), where
I
is the student ID number
(taking values 1
,...,n
) and
J
is the question number (taking values 1
,...,m
). Assume
that all answers are equally likely to be picked. Calculate the joint and the marginal
PMF of
I
and
J
.
(b) Assume that an answer to question
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 Fall '08
 Olvera
 Probability theory, probability density function, stock market trader, ﬁrst mi questions

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