STATISTICS 342  Homework Assignment #1
Due Friday, January 22, 2010
1. Let Y be a uniform random variable with
θ
1
= 0 and
θ
2
= 1.
(a) Using R, generate 10,000 observations of
Y
. Find the following statistics for your 10,000 obser
vations: minimum, maximum, mean and variance. For each statistic, give the theoretical value
that the statistic should be approximately equal to. Then produce a probability histogram of the
10,000 observations.
Turn this histogram in with your assignment.
Describe the histogram in
words.
(b) Take the 10,000 observations of
Y
from part (a) and calculate the following variable:
u
= 3 +
2
y
.
Find the following statistics for your 10,000 observations of this new variable:
minimum,
maximum, mean and variance. Then produce a probability histogram of the 10,000 observation
of this new variable.
Turn in this histogram with your assignment.
Describe the histogram in
words.
(c) Based on your answers to part (b), what distribution do you believe the random variable
U
=
3 + 2
Y
will have? Explain your answer.
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 Spring '08
 Staff
 Statistics, Probability theory, probability density function, Histogram

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