David Troyer
2022-01-17
Answered

What is the formula for the variance of a probability distribution?

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Lakisha Archer

Answered 2022-01-17
Author has **39** answers

Often a shorthand notation is used, where the limits of summation (or integration) are omitted, and sometimes the subscripts;

For a discrete Random Variable X, where:

then the Expectation is defined by:

We get similar results for a continuous Random Variable X, where:

and the Expectation, is defined by (and shorthand):

and the variance is defined by:

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Given an sample of data set X which is normal-distributed to $N(\mu =240,\sigma )$, I want to find the $95\mathrm{\%}$ confidence interval of $max(\mu -200,0)$. As the $max(\mu -200,0)$ cut the normal-distribution curve at the point of 200, the sample of $max(\mu -200,0)$ is not more normal distributed. Therefore what is a reasonable $95\mathrm{\%}$ confidence interval?