Re: [問題] 假設檢定
※ 引述《tyrone208 (等待)》之銘言：
: A random sample of size n=8 is draw from the uniform pdf,f(y;θ)= 1/θ,
: 0<y<θ for the propose of testing
: Ho:θ=2
: H1:θ<2
: at α=0.1 level of significance.Suppose the decision rule is to be based
: on Y8', the largest order statistic,that is Y8'= max(Y1,Y2,...Y8).What
: would be the probability of committing a Type Π error when θ=1.7 ?
先求出f(Yn) = n*[1/θ]*[y/θ]^n-1 = n*[y^n-1/θ^n]
c y^n-1 n y^n c c^n
α= S n*------ dy = -----*-----| = -----= 0.1
0 2^n 2^n n |0 2^n
n
=> c^n = 0.1 * 2^n => c = √0.1 * 2
n
β= P(Yn≧c|θ=1.7)= P(Yn≧√0.1* 2|θ=1.7)
θ=1.7 y^n-1
= S n n * ---- dy ................
√0,1* 2 1.7^n
積分出來n代8進去就求出答案了..0.633!!
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01/07 23:08, , 1F
01/07 23:08, 1F
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