Linear combinations of random variables
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Proof for any continuous random probability distribution
Equations are omitted for technical reasons - download the original pdf
Let X be a continuous random variable with probability density function p(X). Then the expectation and variance of X are defined to be&: [Equation goes here &- download the original to see it.] [Equation goes here &- download the original to see it.] Then [Equation goes here &- download the original to see it.] Also [Equation goes here &- download the original to see it.] Thus, for any random variable, whether discrete or continuous&: [Equation goes here &- download the original to see it.]
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Contents of
Linear combinations of random variables
1 Linear combinations of random variables
2 Independence
3 Scaling and translation of random variable X
4 Proof, for any discrete random probability distribution in general
5 Proof for any continuous random probability distribution
6 Expectation and variance of the linear combination of random variables
7 Form of the linear combination of random variables
8 Scaling and translation of a Normal distribution
9 Linear Combinations of independent Normal distributions
10 Linear combination of independent Poisson distributions.
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