Let Y1, Y2,...Y5 be a random sample of size 5 from a normal population with mean 0 and variance 1.
What is the distribution of ΣYi^2? (Σ, i=1 to 5)
Chi-sq? t? or F? What is its d.f.? Why?
Degree of freedom
2007-01-23 4:30 am
回答 (1)
2007-01-23 5:45 pm
✔ 最佳答案
這個是砌積木問題若果X服從normal population with mean 0 and variance 1.
則X^2服從χ^2(1)
所以Y1, Y2,...Y5 全部服從χ^2(1)
又若X1服從χ^2(m1),X2服從χ^2(m2)
則X1+X2服從χ^2(m1+m2)
所以 ΣYi^2服從χ^2(5)
參考: Introduction to Mathematical Statistics (6th Edition) by Robert V. Hogg, Allen Craig, and Joseph W. McKean
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