Random Variables - Revision history

Admin at 03:42, 5 March 2024

2024-03-05T03:42:39Z

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2024-03-02T01:45:13Z

← Older revision		Revision as of 01:45, 2 March 2024
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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.		Let <math>X,Y</math> be random variables, <math>a, b, c</math> be constants.

	Expectation have the following properties		Expectation have the following properties for linear transformations:

	<math>		<math>
	E(aX + c) = aE(X) + c		E(aX + c) = aE(X) + c
			</math>

			For a linear combination, we have

			<math>
			E(aX + bY) = aE(X) + bE(Y)
	</math>		</math>

	Variance is a bit more complicated. Recall that the calculation of		Variance is a bit more complicated. Recall that the calculation of
	variance involves the average difference from the mean squared.		variance involves the average difference from the mean squared. It is no
			surprise that any constant coefficient is squared, and any translations
			does not impact the spread of data.

	<math>		<math>
	Var(aX + c) = a^2 Var(X)		Var(aX + c) = a^2 Var(X)
			</math>

			For a linear combination, when the two events are independent,

			<math>
			Var(aX + bY) = a^2 Var(X) + b^2 Var(Y)
			</math>

			When the events are dependent,

			<math>
			Var(aX + bY) = a^2 Var(X) + ab Cov(X,Y) + b^2 Var(Y)
	</math>		</math>

2024-03-02T01:41:45Z

← Older revision		Revision as of 01:41, 2 March 2024
Line 1:		Line 1:
	== 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>

2024-03-02T01:38:52Z

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== Linear Combinations of RV ==