Answer:
a) [tex]10[1-e^{-y/3} ] ^{2} e^{-y}[/tex]
b) ≈ 0.76
Step-by-step explanation:
Given that : Y1 < Y2 < Y3 < Y4 < Y5 are the order statistics of five independent observations
mean of θ = 3
a) Determine the P.d.f of the sample median
P.d.f of sample median ( y3 ) = [tex]10[1-e^{-y/3} ] ^{2} e^{-y}[/tex]
attached below is the detailed solution
b) determine the probability that Y4 is < 5
p( Y4 < 5 ) = G4( 5 )
= 0.7599 ≈ 0.76
attached below is the detailed solutions
