Two meteorologists, A and B, wish to determine the annual rainfall depth (θ in mm) over an ungauged region. Meteorologist A has the prior belief θ  N 1850; 302  while meteorologist B believes that θ...

Two meteorologists, A and B, wish to determine the annual rainfall depth (θ in mm) over an ungauged region. Meteorologist A has the prior belief θ

---

N 1850; 302

---

while meteorologist B believes that θ

---

N 1850; 702

---

. A rain gauge is installed in a region. After 1 year, the rain gauge registered the cumulative rainfall of x ¼ 1910. Find the meteorologists’ posterior distributions, considering that the standard error of the annual cumulative rainfall depth is 40 mm and that annual rainfalls are normally distributed, i.e., X  θ

---

N θ; 402