# Mathematische Statistik - Übung Ergänzungsaufgabe 2 Beispiel 3

Two physiscists, A and B want to determine the value of a physical constant. The physicist A with a large experience in the area specifies his prios as $\theta \sim N(900,20^2) \,$. On the other side, physicist B stated a more uncertain prior $\theta \sim N(800,80^2) \,$. Both physicists agree to make an evaluation of $\theta \,$, denoted by X, using a calibrated device with sampling distribution $X|\theta \sim N(\theta, 40^2) \,$. The value $X = 850 \,$ is observed.

(a) What do the physicists infer about $\theta \,$?

Physicist A:


> postmean=function(x,mu,tau,sigma) ((mu/(tau^2)) + (x/(sigma^2))) / (1/(sigma^2) + 1/(tau^2))
>  postvar=function(tau,sigma) 1/(1/(sigma^2) + (1/tau^2))
>
>  postmean(850, 900, 20, 40)
[1] 890
>  postvar(20, 40)
[1] 320
Physicist B:


> postmean=function(x,mu,tau,sigma) ((mu/tau^2) + (x/sigma^2)) / (1/sigma^2 + 1/tau^2)
>  postvar=function(tau,sigma) 1/(1/sigma^2 + 1/tau^2)
>
>  postmean(850, 800, 80, 40)
[1] 840
>  postvar(80, 40)
[1] 1280

(b) Interpret the result.