Consider n independent random variables with gaussian probability densities but with each having its own mean ; and standard deviation o;. Find the probability density of the sum of those n variables as well as its mean and standard deviation.

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Consider n independent random variables with gaussian probability densities but with
each having its own mean t; and standard deviation o;.
Find the probability density of the sum of those n variables as well as its mean and
standard deviation.
Transcribed Image Text:Consider n independent random variables with gaussian probability densities but with each having its own mean t; and standard deviation o;. Find the probability density of the sum of those n variables as well as its mean and standard deviation.
Expert Solution
Step 1

Given that;

Xi~Normal(μi, σi2), i=1, 2,..., n, independently

We know that the moment generating function of the normal distribution is given by;

MX(t)=eμt+12tσ2

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