Stat 5101 (Geyer) Fall 2009
Homework Assignment 11
Due Wednesday, December 9, 2009
Solve each problem. Explain your reasoning. No credit for answers with
no explanation. If the problem is a proof, then you need words as well as
formulas. Explain why your formulas follow one from another.
111.
Suppose the random vector (
X,Y
) has variance matrix
±
4

3

3
9
²
Find sd(
X
), sd(
Y
), and cor(
X,Y
). Note: cor(
X,Y
) is correlation not co
variance.
112.
Suppose sd(
X
) = 5, sd(
Y
) = 7, and cor(
X,Y
) = 2
/
3. Find the
variance matrix of the random vector (
X,Y
).
113.
Suppose
X
has the Poisson distribution with mean 100.
(a) Calculate Pr(
X <
80) exactly.
(b) Calculate Pr(
X <
80) using the normal approximation without correc
tion for continuity.
(c) Calculate Pr(
X <
80) using the normal approximation with correction
for continuity.
(d) Which of (b) and (c) is closer to correct?
(e) Calculate Pr(
X >
120) exactly.
(f) Calculate Pr(
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 Fall '02
 Staff
 Normal Distribution, Standard Deviation, Variance, Probability theory, Normal approximation, Calculate Pr

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