A consistent estimator g Let Y1; Y2; :::; Yn be IID random variables where each random variable has PDF f(y) = y1 for 0 < y < 1, and f(y) = 0 for all other values of y. Also assume that > 0. Show that the sample mean, Y , is a consistent estimator for +1.

E(Y') = ∅/(∅+1), also E(Y) = ∅/(∅+1)

Here sample mean is Y' and population mean is ∅/(∅+1). This means that Y' is a consistent estimator of ∅/(∅+1)

Step-by-step explanation:

I assume your question is:

A consistent estimator g Let Y₁, Y₂, Y₃....Υₙ be IID random variable where each random variable has PDF f(y) = ∅y^(∅ -1) for 0<y<1, and f(y) = 0 for all other values of y

Sample mean, Y is a consistent estimator of ∅/(∅+1) in the attached solution.

1.5, 1.8, 1.23, 1.49, 1.75, 2.4, 2.04, 2.85, 4.2, 5/3, 6/5, 7/2, 7/3, 9/4, 9/5, 12/5, 12/5, 13/9, 15/8, 21/10

This was confusing haha, anyways hope this helped!