## Answers

factorization Theron: Let x,,.. ,Xa denote randon variables with joint probability density fachon beruf) f(x,,.., &n; O) which depends on the parameter O. Then, the statistic = c(x,...X) is sufficerent for o if and only if the pdf (oppuf) can be factured into two components, that is xh(x, , . Xn) os Y Y N N (0,02) al he is known a o2 is unknown Joint density will be 61 619, ,0°) - Genta con tari) ha...

- $ ( (x;.152, 0?) So by boetesiz ata theorem sufficiat for or Go 58,-)) Ś exe-su)" is

GEFORCE CORES b) We have the suffichant statistic We know MUUE is a fuchon of (content the) Soffi creat statis tie such that El 27-M) ²) - E y banue-2a2x] = [E (VI) + nu? - 24 IE (13) T(v()+ (E (7:))) anu - 22 = I (02+u?) on nu? - nor & ne-au- no? & E (Vir mes] = 02 IMVUE is - I Vindest

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