Question

# Moment Generating Functions A student's score on a Psychology exam has a normal distribution with mean...

Moment Generating Functions

A student's score on a Psychology exam has a normal distribution with mean 65 and standard deviation 10. The same student's score on a Chemistry exam has a normal distribution with mean 60 and standard deviation 15. The two scores are independent of each other. What is the probability that the student's mean score in the two courses is over 80?

Before solving, show that the mgf here is an mgf of a Normal distribution. (Biggest confusion)

A student's score on a Psychology exam has a normal distribution .

A student's score on a Chemistry exam has a normal distribution .

The MGF of is

The MGF of is

The MGF is is

The MGF of is

Which is the MGF (since MGF is unique) of normal distribution with mean and variance

Hence the student's mean score in the two courses

Or

The probability,

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