Discrete Random Variable - Revision history

Admin: /* Bernoulli */

2024-03-19T16:34:58Z

Bernoulli

← Older revision		Revision as of 16:34, 19 March 2024
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	== Binomial ==		== Binomial ==

	Repeating a bernoulli experiment <math>b</math> times and we get a '''binomial random variable'''.		Repeating a bernoulli experiment <math>n</math> times and we get a '''binomial random variable'''.

	Consider an experiment with exactly two possible outcomes, conducted n times independently.		Consider an experiment with exactly two possible outcomes, conducted n times independently. The variable of interest <math>X</math> is the number of successful trials. The distribution relies on the number of trials and the probability of success.

	<math>		<math>
	X \sim Binomial(n, p)		X \sim Binomial(n, p)
	</math>		</math>

	~~I'm sleep I'll write the details later. It should be on the equation sheet.~~

	=== PMF ===		=== PMF ===

Admin: /* Binomial */

2024-03-19T16:14:18Z

Binomial

← Older revision		Revision as of 16:14, 19 March 2024
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	I'm sleep I'll write the details later. It should be on the equation sheet.		I'm sleep I'll write the details later. It should be on the equation sheet.

			=== PMF ===

			<math>
			(^n_x) p^x (1 - p)^{n - x}
			</math>

			=== Statistics ===

			<math>
			\mu = np
			</math>

			<math>
			\sigma^2 = np (1 - p)
			</math>

	= Poisson =		= Poisson =

Admin: /* Poisson */

2024-03-19T07:46:34Z

Poisson

← Older revision		Revision as of 07:46, 19 March 2024
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	* The average rate of occurrence per unit of time/sace is the '''rate parameter''' <math>\lambda</math>		* The average rate of occurrence per unit of time/sace is the '''rate parameter''' <math>\lambda</math>

	Poisson distribution approximates binomial distribution when ''n'' is large and ''p'' is small, used to model rare events.		Poisson distribution approximates binomial distribution when ''n'' is large and ''p'' is small, used to model rare events. Normally it is used to measure the number of events in a unit time, whereas [[Continuous Random Variable#Exponential Distribution\|exponential distribution]] models the amount of waiting time until an event.

	I'm sleepy I'll write the details later... zzz...		I'm sleepy I'll write the details later... zzz...

Admin: /* Binomial */

2024-03-19T07:37:05Z

Binomial

← Older revision		Revision as of 07:37, 19 March 2024
Line 57:		Line 57:

	I'm sleep I'll write the details later. It should be on the equation sheet.		I'm sleep I'll write the details later. It should be on the equation sheet.

			= Poisson =
			The '''poisson distribution''' is used when we know the ''average rate of occurrence for a particular event over a particular time period.''

			* There must be '''fixed interval''' of the time or space
			* Events happen with a '''known average rate''' independent of time or the last event.
			* The average rate of occurrence per unit of time/sace is the '''rate parameter''' <math>\lambda</math>

			Poisson distribution approximates binomial distribution when ''n'' is large and ''p'' is small, used to model rare events.

			I'm sleepy I'll write the details later... zzz...

Admin at 07:32, 19 March 2024

2024-03-19T07:32:27Z

@@ Line 1: / Line 1: @@
 [[Category:Statistics]]
 A random variable is '''discrete''' if the values it can take on within an interval is ''finite''.
@@ Line 12: / Line 13: @@
 We usually have tables for these in the case of discrete random variables.

Admin: Created page with "Category:Statistics A random variable is '''discrete''' if the values it can take on within an interval is ''finite''. = PMF and CDF = The '''probability mass function (PMF)''' describes the probability distribution over a discrete random variable. $p(x) = P(X = x)$ The '''cumulative distribution function (CDF)''' specifies the probability of an observation being equal to or less than a given value. $F(x) = P(X \leq x)$ We usually have tabl..."

2024-03-19T06:22:07Z

Created page with "Category:Statistics A random variable is '''discrete''' if the values it can take on within an interval is ''finite''. = PMF and CDF = The '''probability mass function (PMF)''' describes the probability distribution over a discrete random variable. <math>p(x) = P(X = x)</math> The '''cumulative distribution function (CDF)''' specifies the probability of an observation being equal to or less than a given value. <math>F(x) = P(X \leq x)</math> We usually have tabl..."

New page

[[Category:Statistics]]
A random variable is '''discrete''' if the values it can take on within an interval is ''finite''.

= PMF and CDF =
The '''probability mass function (PMF)''' describes the probability distribution over a discrete random variable.

<math>p(x) = P(X = x)</math>

The '''cumulative distribution function (CDF)''' specifies the probability of an observation being equal to or less than a given value.

<math>F(x) = P(X \leq x)</math>

We usually have tables for these in the case of discrete random variables.