Let Y1, Y2, . . . , Yn constitute a random sample from the

QUESTION:

Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) constitute a random sample from the probability density function given by

                                                      \(f(y \mid \theta)=\left\{\begin{array}{ll}\left(\frac{2}{\theta^{2}}\right)(\theta-y), & 0 \leq y \leq \theta \\0 & \text { elsewhere }\end{array}\right.\)

a Find an estimator for \(\theta\) by using the method of moments.

b Is this estimator a sufficient statistic for \(\theta\)

Equation Transcription:

Text Transcription:

Y_1, Y_2, …., Y_n

f(y | theta) = (frac{2}{theta^{2}})(theta - y), & 0 leq y leq theta 0 & elsewhere }.

theta

theta