ISyE 2027
Probability with Applications
Fall 2011
R. D. Foley
Homework 5
September 26, 2011
due Monday
1. Compute
lim
n
→
∞
(
1

3
/n
)
n

1
.
2. Certain distributions turn up so often that they have names. So far, we
have encountered the Bernoulli, binomial and geometric distributions.
For each of the following random variables, if one of the above distribu
tions seems plausible, give the name of that distribution; otherwise, say
none of the three. (a) Whether it rains or not tomorrow on campus on
January 1st, 2012. (b) The number of days starting from Jan. 1st, 2012
until it rains on campus. (c) The number of days in January 2012 that it
rains on campus. (d) Whether the number of days that it rains on cam
pus exceeds 15 or not. (e) The number of days in 2012 until it does not
rain on campus. (f) The amount of rain on January 1st, 2012. In doing
this problem, let us temporarily assume that whether it rains or not on a
particular day is independent of the weather on other days and always
has the same probability
p
.
3. Let
X
be the roll of a fair die.
Let
Y
=
b
X/
3
c
where
b·c
is the “floor
function.” (a) What is the p.m.f. of
Y
? (b) What is the mean of
Y
? (c)
What is the second moment of
Y
?
(d) What is the variance of
Y
?
(e)
What is the standard deviation of
Y
? (f) Suppose you could play a game
where the payoff is
Y
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Zahrn
 Probability, Standard Deviation, Variance, Probability theory, p.m.f.

Click to edit the document details