Let Y 1 , Y 2 , , Y n be a random sample of size n from the pdf f Y (y) (1 )e y , y 0 0 (a) Use moment generating functions to show that the ratio 2nY has a chi square distribution with 2n df (b) Use the result in part (a) to derive a 100(1 ) confidence interval for ...

Let Y 1 , Y 2 , . . . , Y n be a random sample

Question:

Let Y₁, Y₂, . . . , Y_n be a random sample of size n from the pdf

f_Y(y) = (1/θ)e^−y/θ, y > 0; θ > 0

(a) Use moment-generating functions to show that the ratio 2nY̅/θ has a chi square distribution with 2n df.

(b) Use the result in part (a) to derive a 100(1 − α)% confidence interval for θ.

Distribution
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