Let Y,, Y2, .., Yn denote a random sample of size n from a population whose...

Question

Question

Let Y,, Y2, .., Yn denote a random sample of size n from a population whose density is given by Find the method of moments estimator for α.

Answer 1

Answer #1

The mean of the pdf is

.3 .3 3α

Let Y1, Y2, Y3....Yn is a random sample from this distribution. So sample mean is

ar{Y}=rac{Y1+Y2+...Yn}{n}

Since according to method of moments estimators, first theoretical moment is equal to first sample moment so we have

rac{3alpha}{alpha+1}=ar{Y}

3alpha=ar{Y}(alpha+1)

3alpha=ar{Y}alpha+ar{Y}

(3-ar{Y})alpha=ar{Y}

a= (3-Y)

So required estimate is

a= (3-Y)

Answer 2

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