1
Dr. Valerie R. Bencivenga
Economics 329
PRACTICE HOMEWORK #5A:
DISCRETE RANDOM VARIABLES
1.
Each day Alpha Bikeshop sells bicycles according to the following probability distribution:
X = daily number of bikes sold
x
0
1
2
3
4
P
x
(x)
.1
.3
.3
.2
.1
The numbers of bikes sold on different days are statistically independent.
a.
What are the mean and variance of number of bikes sold?
b.
Su
ppose that the bike salesperson’
s
daily income
is $30, plus $20 for each bike sold that
day.
What are the mean
and variance of the salesperson’
s daily income?
c.
What are the mean and variance of income over a
twoday period
(total income)?
How
do they compare with your answers to part b?
d.
Consider
average
income over a twoday period.
What are the mean and variance of
average income?
How do they compare with your answers to part b?
2.
Which of the following are probability functions?
Explain.
a.
otherwise
0
4
,
3
,
2
,
1
x
,
x
)
10
/
1
(
)
x
(
P
i
i
i
X
b.
otherwise
0
10
,...,
3
,
2
,
1
x
,
10
/
1
)
x
(
P
i
i
X
c.
otherwise
0
...
,
3
,
2
,
1
x
,
2
.
)
x
(
P
i
x
i
X
i
3.
This problem continues from problem 2 of Assignment #3.
a.
Define a random variable
X
= number of hits in three attempts.
Give the probability
distribution of
X.
b.
Does
)
win
(
P
2
X
P
?
Explain.
(Recall you calculated
win
P
in Practice Homework
#4a, problem 2.)
c.
Is
X
a binomial random variable?
Explain.
4.
An insurance company is interested in the joint probability distribution of
X
= number of cars
and
Y
= number of drivers.
The table below gives the relative frequencies obtained from a large
random sample of households.
These relative frequencies may be interpreted as probabilities.
a.
What is the probability that a randomlychosen household has two cars and one driver?
b.
What is the expected number of drivers?
What is the variance of number of drivers?
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 Spring '12
 BENCIVENGA
 Economics, Probability, Probability theory, insurance company

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