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Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of five independent observations from an exponential distribution that has a mean of θ = 3. (a) Find the p.d.f. of the sample median Y3. (b) Compute the probability that Y4 is less than 5.

Sagot :

batolisis

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

View image batolisis
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