Q3. Let X1,...,Xn be independent random variables each with Poisson(Xi) distributions for i= 1,...,n. Given Bayesian view: ().1,..,An) are realizations from independent Gamma (oi,1) variables, Li, for i= 1,....n serving as prior distributions. So: (X1,...,Xn) |L1=Al,..,Ln=An , are conditionally independent Poisson(Xi) as specified above. a. Please show the calculations and find the joint prior distribution of: LA , i= 1,. ..,n) b. Please show calc and find posterior distribution of (P1,....,Pn) given X1 = ml,..... .,Xn = mn