a.
Prove that the moment-generating
a.
Explanation of Solution
From the given information, X follows Poisson distribution with parameter
The moment generating function of X is
Then,
Hence proved
b.
Prove that
b.
Explanation of Solution
From the given information, the expansion is
From the part a
Then,
As
Hence proved.
c.
Prove that the distribution function of Y converges to a standard
c.
Explanation of Solution
From the theorem 7.5, if Y and
From the part b, as
This is the moment generating function of the standard normal distribution.
By using theorem 7.5,
Hence proved.
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Chapter 7 Solutions
Mathematical Statistics with Applications
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