Suppose Y_(1),Y_(2),dots,Y_(5) are mutually independent lug nut lifetimes.
Assume each lug nut has probability density function (pdf)
fy(y)= { 3y^2, 0<1<1
{ 0, otherwise.
If the lug nuts are in a serie system, lifetime is determined by {Y_((1))=min{Y_(1),Y_(2),dots,Y_(5)} the system fails when the first nut fails. Find the pdf of Y(1).
If the lug nuts are arranged in a parallel system. Lifetime determined by.
Y_((5))=max{Y_(1),Y_(2),dots,Y_(5)}. The system will fail when the last lug nut fails. Find the pdf of Y(5).
Find the pdf of the sample median Y(3) and calculate P(Y_((3))>0.5)
