Question

Questions start here:

Make use of the following: (a) Some probabılty densıty functions (1) 1fX ~ N (μ σ2) the probability density functlon is (n) If X~beta I (m, n) the probabılıty densıty function is (111) IfX ~ X2 (n, δ) the probability density function is (iv) If X~ Fmn(S) the probabılıty density function is 「 (m + n + 2k) x2(m+2k)- k1 (b) Some mathematıcal functions -00 (n) Γ (n)a-n-fe-arx"-'dx 0 (iv) iv) Г (n)「(m) n + m - ( - a)2 - a1 (vn) x2-2ax (vii) fl f1 CO (ix) e* - に0 (n + k) (ax) Distribution Theory QUESTION 1 (a) Let Xi ~ N (A-1) ( 1, 2, n) where Xi, X2, , Xn are independent. Name the distrib- ution of Σ X, with its parameters. (b) If X ~ χ2 (n, δ) find the expected value of X where E (x) = f c xfx (x) dx. (c) Let X ~ N (δ, 1) and S2 ~ χ2 (n) where X and S2 are independently distributed 0) Name the distribution of A with its parameters (i) Find the EX

Answer 1

2. We hane to finet mean o Yhe chi- square disti butiom fanction

e趸 a (1-2t 2 2. 2. I 사-coutticient at tr in he expansion endintly distibuted X and Sz am İndutend intly distributed dismbuuted

Ratio ot standard nonmal vawate to Chi-souare vasvate avad by ito deg Cista buton レっ olis ti buhim a synmeric and Sene