You created a random number generator that works as follows:(adsbygoogle = window.adsbygoogle || []).push({});

With probability p it selects a number X from the standard normal distribution N(0,1), and

with complimentary probability (1-p) it selects a random number X from an off-central

normal distribution N(5, 1). Write the distribution function of X.

How would you attempt this.

Obviously the variance increases.

and the mean is a weighted average of the two.

but as far as getting fx(x) I am stumped.

Is it correct to add the two distributions together and simplify?

(p)*N(0,1) + (1-p)*N(5,1)

using the gaussian equation?

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# Distribution of weighted Normal Distributions

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