Use the heuristic argument to show that the joint pdf of
Chapter 6, Problem 10E(choose chapter or problem)
Use the heuristic argument to show that the joint pdf of the two order statistics \(Y_{i}<Y_{j}\) is
\(g\left(y_{i^{\prime}} y_{j}\right)=\frac{n !}{(i-1) !(j-i-1) !(n-j) !}\)
\(\begin{aligned}&\times\left[F\left(y_{i}\right)\right]^{i-1}\left[F\left(y_{j}\right)-F\left(y_{i}\right)\right]^{j-i-1} \\&\times\left[1-F\left(y_{j}\right)\right]^{n-j} f\left(y_{i}\right) f\left(y_{j}\right),-\infty<y_{i}<y_{j}<\infty\end{aligned}\)
Equation Transcription:
Text Transcription:
Y_i<Y_j
g(y_i,y_j)= n!/(i-1)!(j-i-1)!(n-j)!
x[F(y_i)^i-1[F(y_j)-F(y_i)]^j-i-1
x[1-F(y_j)^n-j f(y_i)f(y_j),- infinity <y_i<y_j< infinity
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