Concept explainers
a.
Prove that the method-of-moments estimators for the standard deviations of X and Y are
a.
Explanation of Solution
It is given that the
It is noted that in the method of moments, the sample moments provide good estimates of the population moments.
The sample moments are as follows:
Population moments are as follows:
The sample variance is the good estimates of the population variance.
The method-of-moments estimator for the standard deviation of X is as follows:
The standard deviation of Y is as follows:
Thus, it is proved that the method-of-moments estimators for the standard deviations of X and Y are,
b.
Find the method of moment’s estimator for
Compare the estimator to
b.
Explanation of Solution
From Part (a), it is seen that method-of-moments estimators for the standard deviations of X and Y are as follows:
The method of moment’s estimator of
Now, substitute the above estimators in the following formula:
Thus, the method of moment’s estimator for
Hence, the method of moment’s estimator for
Want to see more full solutions like this?
Chapter 11 Solutions
Mathematical Statistics with Applications
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,