考試抑鬱發癲症持續發作

The number of exam practice questions Connie gets done in a day has a mean of u and a variance of 100.
u has a mean of 15 and a variance of 5.
Connie got 15 questions done yesterday and 2 questions today. Find the expected number of questions she will get done tomorrow using Buhlmann credibility.

Soln:
Mu = E[E[X|u]] = E[u] = 15
v = E[Var(X|u)] = E[100] = 100
a = Var(E[X|u]) = Var(u) = 5
k = v/a = 20
Z = 2/(2+20) = 0.091
Xbar = 8.5
X = (0.091)*8.5 + (1-0.091)*15 = 14.4091

Therefore the expected number of questions Connie will get done tomorrow is 14.4091.