Linear combinations of random variables
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Scaling and translation of a Normal distribution
Equations are omitted for technical reasons - download the original pdf
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.]
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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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