Linear combinations of random variables
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Proof, for any discrete random probability distribution in general
Equations are omitted for technical reasons - download the original pdf
Let X be a discrete random variable. Let P(X = Xi) be the probability that X takes the value xi. Then, in general, the expectation, E(X) and variable Var(X) are defined to be [Equation goes here &- download the original to see it.] We abbreviate these to [Equation goes here &- download the original to see it.] and [Equation goes here &- download the original to see it.] respectively. Then [Equation goes here &- download the original to see it.] [Equation goes here &- download the original to see it.] Also [Equation goes here &- download the original to see it.] The first proof is just a particular case of this more generalised proof for any discrete random variable.
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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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