Concept explainers
a.
Verify that
a.
Explanation of Solution
Consider two independent random samples of size
The mean and variance for
The mean and variance for
Therefore, it is verified that
b.
Verify that
b.
Explanation of Solution
Note that the statistic
Consider the following for two independent random samples of size
It is known that the above expression is a linear combination of square of independent variables from normal distribution. Thus, by definition of chi-square distribution, the sum of the two statistics has the
Therefore, it is verified that
c.
Verify that
c.
Explanation of Solution
Note that the statistic
Thus, consider the following:
It is solved as follows:
The above expression follows Student t distribution with
d.
Compute
d.
Answer to Problem 128SE
The
Explanation of Solution
The
Therefore, the
e.
Explain the Parts (a)–(d), by substituting k=1.
e.
Explanation of Solution
If k=1, Part (a) becomes
If k=1, Part (b) becomes
If k=1, Part (c) becomes
If k=1, the
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Chapter 8 Solutions
Mathematical Statistics with Applications
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