Let X have a probabiltiy density function fX(x)={ (2(θ−x)) /θ^2 , 0<x<θ 0, otherwise. (a) Show...

Question

Question

Let X have a probabiltiy density function

fX(x)={ (2(θ−x)) /θ^2 , 0<x<θ

0, otherwise.

(a) Show that X has distribution function

FX(x)=⎨0 , x ≤ 0

((2x)/θ) − ((x^2)/(θ^2)) , 0 < x < θ

1 , x ≥ θ

(b) Show that X/θ is a pivotal quantity.

(c) Us the pivotal quantity from part (b) to find a 90% lower confidence limit for θ

Answer 1

Answer #1

Answer 2

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