ISS Statistics Paper II (Old Subjective Pattern): Questions 38 - 39 of 39

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 39 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 200.00 or

Question number: 38

» Hypotheses Testing » Uniformly Most Powerful Test

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Fins a Most powerful test for testing the simple hypothesis H0:σ2=σ02 against the simple alternative hypothesis H1:σ2=σ12 based on n random observations from N (µ, σ 2) where µ is know. Show that this MP test is UMP (Uniformly most powerful).

Explanation

Let X i ’s are n random observations from N (µ, σ 2) and the pdf is

f(x_)=(2πσ2)n2exp{12σ2i=1n(xi… (532 more words) …

Question number: 39

» Multivariate Analysis » Wishart's Distribution » Reproductive Properties

Appeared in Year: 2015

Essay Question▾

Describe in Detail

(i) Let A i be distributed as Wishart Wmi(Ai Σ) , i = 1, 2 and A 1, A 2 be independent. Show that A 1 +A 2 is distributed as Wm1+m2(A1+A2 Σ) .

(ii) If A is distributed as Wm(A Σ) , then CAC’ is distributed as Wm(CAC CΣC) where C is a nonsingular matrix of order m.

Explanation

(i) We have A1~Wm1(A1Σ) that is

A1=i=1m1YiYi where Yi~N(0,Σ) and Y i ’s are independent.

Similarly, A2~… (350 more words) …

f Page
Sign In