If Y1, Y2, . . . , Yn denote a random sample from a

Chapter 9, Problem 42E

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QUESTION:

If \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from a geometric distribution with parameter , show that \(\bar{Y}\) is sufficient for .

Equation Transcription:

Text Transcription:

Y1, Y2,...,Yn

\bar Y

Questions & Answers

QUESTION:

If \(Y_{1}, Y_{2}, \ldots, Y_{n}\) denote a random sample from a geometric distribution with parameter , show that \(\bar{Y}\) is sufficient for .

Equation Transcription:

Text Transcription:

Y1, Y2,...,Yn

\bar Y

ANSWER:

Step 1 of 4

It is given that  be the random sample from the geometric distribution with parameter .

We need to determine   is sufficient for .

The probability mass function of geometric distribution is,

 

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