Linear combinations of random variables
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Expectation and variance of the linear combination of random variables
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Let X and Y be random variables with expectations E(X) and E(Y) and variances Var(X) and Var(Y) respectively. Let a and b be constants. Then [Equation goes here ; ; download the original to see it.] Also, if X and Y are independent [Equation goes here ; ; download the original to see it.] The proofs of these results are advanced and we only illustrate these formulae at this stage. Example The random variables X and Y are independent with E(X) = , Var(X) = 0. ; E(Y) = 2, Var(Y) = . Find the expectation and variance of (a) 2X + Y, (b) ½X ; ;2Y [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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