Find the 60th percentile of the following distributions: (a) Exponential with mean θ (b) Continuous uniform...

Question

Question

Find the 60th percentile of the following distributions: (a) Exponential with mean θ (b) Continuous uniform on [1,5] (c) f (x)= (x+1)/2 ,−1< x <1

Answer 1

Answer #1

a) for exponentila distribution:

F(x) =1-e^-x/

let 60th percentile is a ;

F(a) 1-e^-a/=0.6 or e^-a/=0.4

taking long on both sides

a =-*ln(0.4)

b)

F(a) =(a-1)/(5-1) =(a-1)/4 =0.6

a-1 =2.4

a =2.4+1 =3.4

c)

F(a) = f(x) dx = (x+1)/2 dx =(x²/2+x)/2|^a_-1 =0.6

(a² /2+a)/2+1/4 =0.6

a²+2a-1.40 =0

solving above a =0.5492

Answer 2

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