Linear combinations of random variables
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Form of the linear combination of random variables
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The above results apply generally to all random variables regardless of the form of their distribution. However, we are interested in the form the linear combination of two random variables takes ; ; that is, in the nature of the distribution that arises when two distributions are combined in some way. Here we state without proof three results and illustrate each in turn.
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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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