Random Variable - Revision history

Rice at 19:35, 17 May 2024

2024-05-17T19:35:45Z

← Older revision		Revision as of 19:35, 17 May 2024
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			[[Category:Statistics]]

	A '''random''' variable is a numerical variable whose outcome is the result of a random process (i.e. we don't know what will happen for certain). Notably, the numerical interpretation of the outcome of an [[Probability#Experiment and Events\|experiment]] is a random variable. They come in two types, deserving their own pages. See		A '''random''' variable is a numerical variable whose outcome is the result of a random process (i.e. we don't know what will happen for certain). Notably, the numerical interpretation of the outcome of an [[Probability#Experiment and Events\|experiment]] is a random variable. They come in two types, deserving their own pages. See

Admin: /* Linear Combinations */

2024-03-19T06:39:01Z

Linear Combinations

← Older revision		Revision as of 06:39, 19 March 2024
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	The expectation is		The expectation is


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

			whereas the variance is

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

			I'm sleepy so I'm not gonna derive this one.

Admin: /* Linear Combinations */

2024-03-19T06:38:04Z

Linear Combinations

← Older revision		Revision as of 06:38, 19 March 2024
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	where ''a'' and ''b'' are constants. They are ''not'' [[bivariate]]		where ''a'' and ''b'' are constants. They are ''not'' [[bivariate]]

			The expectation is


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

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

Admin at 06:36, 19 March 2024

2024-03-19T06:36:49Z

← Older revision		Revision as of 06:36, 19 March 2024
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	Var(aX + c) = a^2 Var(X)		Var(aX + c) = a^2 Var(X)
	</math>		</math>

			= Linear Combinations =
			A '''linear combination''' of random variables <math>X</math> and <math>Y</math> is given as

			<math>aX + bY</math>

			where ''a'' and ''b'' are constants. They are ''not'' [[bivariate]]

Admin: /* Statistics */

2024-03-19T06:35:04Z

Statistics

← Older revision		Revision as of 06:35, 19 March 2024
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	When we are interested in the variability of a random variable, we look at the '''variance''' and the '''standard deviation''': the latter being the expected difference from mean, and the former being the square of the latter (not really used for interpretation, more for math).		When we are interested in the variability of a random variable, we look at the '''variance''' and the '''standard deviation''': the latter being the expected difference from mean, and the former being the square of the latter (not really used for interpretation, more for math).

			= Properties of Statistics =
			I'm just gonna start writing equations.

			<math>
			E(c) = c
			</math>

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

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

			<math>
			Var(X) = E((X - \mu)^2) = E(X^2) - E(X)^2
			</math>

			Cool name for this: the ''law of the unconscious statistician'' for how obvious it is
			<math>
			E(g(X)) = \sum g(x_i) P(X = x_i)
			</math>

			<math>
			Var(c) = 0
			</math>

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

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

Admin: Created page with "A '''random''' variable is a numerical variable whose outcome is the result of a random process (i.e. we don't know what will happen for certain). Notably, the numerical interpretation of the outcome of an experiment is a random variable. They come in two types, deserving their own pages. See = Statistics = Random variables has several statistics that we care about. See pages Continuous Random Variable and Discrete Random Var..."

2024-03-19T06:30:05Z

Created page with "A '''random''' variable is a numerical variable whose outcome is the result of a random process (i.e. we don't know what will happen for certain). Notably, the numerical interpretation of the outcome of an experiment is a random variable. They come in two types, deserving their own pages. See = Statistics = Random variables has several statistics that we care about. See pages Continuous Random Variable and Discrete Random Var..."

New page

A '''random''' variable is a numerical variable whose outcome is the result of a random process (i.e. we don't know what will happen for certain). Notably, the numerical interpretation of the outcome of an [[Probability#Experiment and Events|experiment]] is a random variable. They come in two types, deserving their own pages. See

= Statistics =
Random variables has several statistics that we care about. See pages [[Continuous Random Variable]] and [[Discrete Random Variable]] for how to calculate these values.

When we are interested in the average outcome of a random variable, we look at the '''expected value''' (mean): a weighted average of the possible outcomes.

When we are interested in the variability of a random variable, we look at the '''variance''' and the '''standard deviation''': the latter being the expected difference from mean, and the former being the square of the latter (not really used for interpretation, more for math).