If Y is a continuous random variable and m is the median

Chapter 6, Problem 82E

(choose chapter or problem)

If  Y is a continuous random variable and m is the median of the distribution, then m is such

that \(P(Y \leq m)=P(Y \geq m)=1 / 2\). If \(\mathrm{Y}_{1}, \mathrm{Y}_{2}, \ldots, \mathrm{Y}_{\mathrm{n}}\) are independent, exponentially distributed random variables with mean \(\beta\) and median m, Example 6.17 implies that \(\mathrm{Y}(\mathrm{n})=\max \left(\mathrm{Y}_{1}, \mathrm{Y}_{2}, \ldots, \mathrm{Y}_{\mathrm{n}}\right)\) does not have an exponential distribution. Use the general form of  \(F_{y_{(n)}}(\mathrm{y})\) to show that

\(P(Y(n)>m)=1-(.5)^{n}\)

Equation Transcription:

Text Transcription:

P(Y \leq  m) = P(Y \geq  m) = 1/2.

Y1, Y2,....,Yn

\beta

Y(n)=max (Y1, Y2,....,Yn

Fy(n)(y)

P(Y(n) >m)=1-(.5)n