Additivity of the Normal Distribution

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The probability function for the normal distribution with expectation value (mu) and standard deviation T is:
(Please use Maple-notation in the input field!)


(a)

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Especially important is the standard normal distribution N(0,1) with probability density function


(b)

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An important characteristic of the normal distribution is its additivity.



(c)

The sum of two independent normal distributed random variables and is ___________________ distributed, with
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(d)

Let be a normal distributed random variable
is ___________________ distributed with
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