Question

2. Let X1, .., X6 be i.i.d from Pois() with 2 with pdf 20. Suppose A has the prior Gamma(a,B) _ Aa-1e-1в Г(а) т(A) - where a 10, 3 = 4 (i) Find the Bayes Estimate of A (ii) Find a 90% credible interval for A (Use the x2 table and equal tail areas)

Answer 1

Tope Page 1ubhash. Date U CtTEBre 2 cal Ka s Pn ) 02 have Xi are ftd traefas Ltu Noww. the poahanoe detn buhan ah A/p Ltkelihoad xbaor Lrelthoad ylnchon tat tatu

Page a 2ッbhash Page Date Q2a) cantd Estu the pner diatn'buhen 04 A e x the beatenae Autr'buhen a .XA AP taレ nla)

PAge 3 Page L lubhash CHE J Date L cOnfd e ohere Ct A Gamna Henaar the Rayes echmote of uder quadraha loe 1a the Paatener mean Bayec

Page 4 CHE Page L ubhash JL Date la) A XBayes l0 20 +4 ABauee Bayes Hene the Rayea eehmake ofy pefea

Page OHEAG Page ubhash Date the bootenar utorbuhon o2 hare Xn LCAla afg AlK A) ngamua lot20, 6+4 org (alx Xn Abamna Gama 0,16 Noe 4x.. xn he n P O.90 e the contgrdena mie fror A re

Page 6 ubhash Page L J Date 20 P 0.40 o.90 Cy 269D . eo tablee DO .90 C2

Jubhash PageL Date L CHEES Ct 43.18196 79.0814 4- PE 43.18796 4ZVA o 19.0819 4- .90. 43. 18746 79.0814 0.90 P 43.18746L 20A L14.08114 O40 42.1871b L19.081(94 20 ap P2 15 9348 3.954093 240

Pase Page3 ubhash CHEES Date Heree the 90% CeArte Intenal tr L 4 3.95404. 2.159398