Linear combinations of random variables DOWNLOAD FREE

Scaling and translation of a Normal distribution If X has a Normal distribution, then so does aX + b [Equation goes here ; ; download the original to see it.] Example A company produces plastic wallets. Let X represent the width of the wallets. It is given that X is normally distributed with mean 2cm and variance 0. cm. The machine is recalibrated to give a new width Y = 2X ; ; 10 cm. State the distribution of Y. Find the probability that the new wallets will be within 1.0cm of their expected mean. [Equation goes here ; ; download the original to see it.] [Diagram goes here ; ; download the original to see it.] We require [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