Suppose that X is a continuous random variable with p.d.f. 2x (x/0)° S(x;0) = e ,x>0,0 > 0 ssume that we have a random sample of size n. Derive the generalized likelihood ratio test of Họ:0=0

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Suppose that X is a continuous random variable with p.d.f.
2x (x/0)
S(x:0) = 2Awo°
e
,x> 0,0 > 0
Assume that we have a random sample of size n.
Derive the generalized likelihood ratio test of Ho:0=0 against
H:0> 0, based on a random sample of size n.
Find the power function of the test. Explain why we need to calculate the
power function of the test?
Transcribed Image Text:Suppose that X is a continuous random variable with p.d.f. 2x (x/0) S(x:0) = 2Awo° e ,x> 0,0 > 0 Assume that we have a random sample of size n. Derive the generalized likelihood ratio test of Ho:0=0 against H:0> 0, based on a random sample of size n. Find the power function of the test. Explain why we need to calculate the power function of the test?
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