Tom rolls 2 fair dice and adds the results from each. Work out the probability of getting a total more than 4.

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liamgreene90

24.04.2021

Mathematics

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.

$m_D(u)=E(e^{uD})=e^{18u^2+10u}...(1)$

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

The general moment generating function is :

$m_D(u)=E(e^{uD})=e^{\frac{1}{2}\sigma^2u^2+\mu u}...(2)$

(a)

Now, compare the equation (1) and (2) we get,

$\mu=10$

Therefore, the expected value of the distance north from city centre archaeologists will have to travel to find the temple is 10 miles.

(b)

Now, compare the equation (1) and (2) we get,

$\frac{1}{2}\sigma^2=18$

$\Rightarrow \sigma^2=18\times 2=36$

$\Rightarrow \sigma=\sqrt{36}=6$

Therefore, the standard deviation of that distance is miles.

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