Continuous Random Variable - Revision history

Rice: /* Probability Density Function f(x) */

2024-04-25T04:08:31Z

Probability Density Function f(x)

← Older revision		Revision as of 04:08, 25 April 2024
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	* Probability becomes area under a curve		* Probability becomes area under a curve

	= Probability Density Function ~~<math> f(x) </math>~~ =		= Probability Density Function =

	The probability density function (pdf) maps a continuous variable to a		The probability density function (pdf) maps a continuous variable to a

2024-03-19T07:50:09Z

Normal Random Variable

← Older revision		Revision as of 07:50, 19 March 2024
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	= Normal Random Variable =		= Normal Random Variable =
	[[File:Z score table.png\|thumb\|Z score table]]		[[File:Z score table.png\|thumb\|Z score table]]
	Normal random variables are the most widly used continuous RV in		'''Normal random variables''' (aka. Gaussian RV) are the most widly used continuous RV in
	statistics, characterizing many natural phenomenons. It is the famous		statistics, characterizing many natural phenomenons. It is the famous
	bell curve.		bell curve.

2024-03-19T07:49:17Z

Exponential Distribution

← Older revision		Revision as of 07:49, 19 March 2024
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	* At a constant average rate		* At a constant average rate

	It takes in one parameter: <math>\lambda</math>, the rate parameter. It		It takes in one parameter: <math>\lambda</math>, the '''rate parameter.''' Defined by the mean below, it is the ''average rate per unit time/space.''
	~~is defined~~ by the mean below.

	Exponential distribution has the '''memoryless property''': the		Exponential distribution has the '''memoryless property''': the

2024-03-19T07:46:12Z

Probability Distribution Function f ( x ) {\displaystyle f(x)}

← Older revision		Revision as of 07:46, 19 March 2024
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	* Probability becomes area under a curve		* Probability becomes area under a curve

	= Probability ~~Distribution~~ Function <math> f(x) </math> =		= Probability Density Function <math> f(x) </math> =

	The probability density function (pdf) maps a continuous variable to a		The probability density function (pdf) maps a continuous variable to a
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	The mean and variance calculations are pretty much the same as that of		The mean and variance calculations are pretty much the same as that of
	discrete random variables, except the summations are swapped out for		[[Discrete Random Variable\|discrete random variables]], except the summations are swapped out for
	integrals.		integrals.

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	</math>		</math>

	= Exponential Distribution ~~<math>X \sim Exp(\lambda)</math>~~ =		= Exponential Distribution =

	The exponential distribution models events that occurs		The exponential distribution models events that occurs
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	</math>		</math>

	Notably, it models time until some event has happened.		Notably, it models time until some event has happened, in contrast to [[Discrete Random Variable#Poisson\|poisson distribution]], which measures the number of events in a unit time.

	==== PDF ====		==== PDF ====

2024-03-19T06:22:54Z

← Older revision		Revision as of 06:22, 19 March 2024
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			[[Category:Distribution (Statistics)]]
	Continuous random variables have an inifinite number of values for any		Continuous random variables have an inifinite number of values for any
	given interval. While similar, the approach to analysis is very		given interval. While similar, the approach to analysis is very

2024-03-18T17:46:24Z

← Older revision		Revision as of 17:46, 18 March 2024
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	W \sim N(a\mu)X + b\mu_y, a^2 \sigma^2_X + b^2 \sigma^2_y)		W \sim N(a\mu)X + b\mu_y, a^2 \sigma^2_X + b^2 \sigma^2_y)
	</math>		</math>

			= Other distributions =

			[[Two Numerical RVs]]

	[[Category:Statistics]]		[[Category:Statistics]]

2024-03-09T05:36:27Z

Normal Random Variable

← Older revision		Revision as of 05:36, 9 March 2024
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	= Normal Random Variable =		= Normal Random Variable =
			[[File:Z score table.png\|thumb\|Z score table]]
	Normal random variables are the most widly used continuous RV in		Normal random variables are the most widly used continuous RV in
	statistics, characterizing many natural phenomenons. It is the famous		statistics, characterizing many natural phenomenons. It is the famous

2024-03-05T03:36:22Z

← Older revision		Revision as of 03:36, 5 March 2024
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	W \sim N(a\mu)X + b\mu_y, a^2 \sigma^2_X + b^2 \sigma^2_y)		W \sim N(a\mu)X + b\mu_y, a^2 \sigma^2_X + b^2 \sigma^2_y)
	</math>		</math>

			[[Category:Statistics]]

2024-03-02T06:19:12Z

← Older revision		Revision as of 06:19, 2 March 2024
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	==== Standard Normal Table ====		==== Standard Normal Table ====
	~~[[File:Standard Normal Distribution Table.png\|thumb\|Standard normal distribution table for left tail]]~~
	The standard normal table calculate lower tail values based on the		The standard normal table calculate lower tail values based on the
	standard normal distribution (i.e. area under the curve left of the		standard normal distribution (i.e. area under the curve left of the
	point).		point).

			==== Linear Combinations of Independent Normal RV ====

			<math>
			W = aX + bY
			</math>

			<math>
			W \sim N(a\mu)X + b\mu_y, a^2 \sigma^2_X + b^2 \sigma^2_y)
			</math>

2024-03-02T06:15:29Z

Standard Normal Table

← Older revision		Revision as of 06:15, 2 March 2024
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	==== Standard Normal Table ====		==== Standard Normal Table ====
			[[File:Standard Normal Distribution Table.png\|thumb\|Standard normal distribution table for left tail]]
	The standard normal table calculate lower tail values based on the		The standard normal table calculate lower tail values based on the
	standard normal distribution (i.e. area under the curve left of the		standard normal distribution (i.e. area under the curve left of the
	point).		point).