Practice Midterm Exam Questions  Second Midterm
Two Random Variable Questions.
1. Using the distribution in Question 512, part c) (p168)
a)
Work out the mean and variance of (X+Y).
b)
Work out the mean and variance of X, then the variance of Y.
c) What is the relationship between the answers in a) and b)?
(Note: This is simply done using the spreadsheet, where you can set up tables for each distribution and
use the copy command and the fill down command to quickly replicate similar instructions. I will make
such questions simple to calculate on an exam).
2. Suppose that the random variable X measures number of hamburgers purchased in a restaurant in an
hour and Y measures the number of packages of antacid purchased in the convenience market next door
in the same hour.
The correlation between the two variables is 0.75.
(a) Interpret what this correlation tells us about the relationship between the number of hamburgers
purchased and the number of antacids purchased (be thorough in your answer).
(b) Suppose the variance of X and the variance of Y are both equal to 16.
What is the covariance
between X and Y.
(c) What is the variance of (X + Y)?
3. The joint distribution of two random variables X and Y is given by
Y
X
1
2
1
0.05
0.05
2
0.5
0.3
3
0.05
0.05
(a) What is the marginal distribution of X?
(b) What is the mean of X?
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 Spring '09
 ichigaara
 Standard Deviation, Variance, Probability theory, researcher

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