Random Variables: Difference between revisions
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= 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.
