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== Linear Combinations of RV ==
= Linear Combinations of RV =
 
Let <math>X</math> be a random variable, <math>a, c</math> be constants.
 
Expectation have the following properties
 
<math>
E(aX + c) = aE(X) + c
</math>
 
Variance is a bit more complicated. Recall that the calculation of
variance involves the average difference from the mean squared.
 
<math>
Var(aX + c) = a^2 Var(X)
</math>

Revision as of 01:41, 2 March 2024

Linear Combinations of RV

Let Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} be a random variable, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a, c} be constants.

Expectation have the following properties

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E(aX + c) = aE(X) + c }

Variance is a bit more complicated. Recall that the calculation of variance involves the average difference from the mean squared.