Concept explainers
a.
Prove that
a.
Answer to Problem 100E
It is proved that
Explanation of Solution
It is given that
Poisson distribution:
Let X be a discrete random variable and is said to follow Poisson distribution if its probability mass
Consider,
It is known that,
Thus, it is proved that
b.
Prove that
b.
Explanation of Solution
Calculation:
It is given that for
From the PMF given in Part (a),
Where Y follows Gamma distribution with
Similarly,
Where Y follows Gamma distribution with
Hence, it is proved that
c.
Prove that
Explain the answer.
c.
Explanation of Solution
From Part (b), it is obtained that that
Now,
Hence, it is proved that
d.
Interpret the result of Part (c).
d.
Explanation of Solution
From Part (c), it is proved that
Hence, it can be said that the Poisson distribution which has greater mean has the smaller cumulative probability value for any constant k, such that
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Chapter 4 Solutions
Mathematical Statistics with Applications
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