Linear combinations of random variables DOWNLOAD FREE

Expectation and variance of the linear combination of random variables 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.]

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.

Related articles: (1) Discrete probability distribution, (2) The central limit theorem