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
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