The ancient Temple of Thos is believed to be buried near the north-south directed main canal through the modern city of Gyre. There is considerable uncertainty, though as to where. A probabilist believes that the distance D of the temple in miles north from the center of Gyre follows a moment generating function mD(mu) = E(euD) = e18u2 + 10 u
a) Find the expected value of the distance north from city center archaeologists will have to travel to find the temple.
b) Find the standard deviation of that distance.

Hence, the expected value of the distance north from city centre archaeologists will have to travel to find the temple is miles and the standard deviation of that distance is miles.

Step-by-step explanation:

Given :

Moment generating function.

Any two functions can not have the same moment generating function.

The general moment generating function is :

(a)

Now, compare the equation and we get,

Therefore, the expected value of the distance north from city centre archaeologists will have to travel to find the temple is

(b)

Now, compare the equation and we get,

Therefore, the standard deviation of that distance is miles.

step-by-step explanation: