How would you solve the following? I am mostly lost in regards to what is asking

ID: 3394101 • Letter: H

Question

How would you solve the following? I am mostly lost in regards to what is asking, please help thank you

A language teacher gives her course an test with two parts:

a conversation test worth 50 points and a written test worth 50

points. Suppose that the grades on the conversation test are normally

distributed with mean 35 and variance 36, and the grades on the written

component are normally distributed with mean 40 and variance 25. Suppose

that the scores on the two components are independent. How can we describe

the distribution of scores on the exam as a whole? (THis must be answered in one line)

Let scores in conversation test be denoted by C, and written test be denoted by W:

Total Score (T) = C+W

E[T] = E[C+W] = E[C] + E[W] = 35+45 = 75

Var[T] = Var[C] + Var[W] + 2Cov(C,W)

Cov(C,W) = 0 as the 2 scores are independent.

So, Var[T] = 36+25 = 61

One line Answer: Total Score is normally distributed with mean 75 and variance 61.

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