Linear combinations of random variables DOWNLOAD FREE

Proof for any continuous random probability distribution 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.]

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