KermMartian at 19:11, 24 February 2016

2016-02-24T19:11:45Z

← Older revision		Revision as of 19:11, 24 February 2016
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	Going off of the relationship between geometpdf( and geometcdf(, we can write a formula for geometcdf( in terms of geometpdf(:		Going off of the relationship between geometpdf( and geometcdf(, we can write a formula for geometcdf( in terms of geometpdf(:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\operatorname{geometcdf}(p,n) = \sum_{i=1}^{n} \operatorname{geometpdf}(p,i) = \sum_{i=1}^{n} p\,(1-p)^{i-1}		\operatorname{geometcdf}(p,n) = \sum_{i=1}^{n} \operatorname{geometpdf}(p,i) = \sum_{i=1}^{n} p\,(1-p)^{i-1}
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	(If you're unfamiliar with sigma notation, <math>\sum_{i=1}^{n}</math> just means "add up the following for all values of i from 1 to n")		(If you're unfamiliar with sigma notation, <math>\sum_{i=1}^{n}</math> just means "add up the following for all values of i from 1 to n")
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	However, we can take a shortcut to arrive at a much simpler expression for geometcdf(. Consider the opposite probability to the one we're interested in, the probability that it will '''not''' take "at most N trials", that is, the probability that it will take more than N trials. This means that the first N trials are failures. So geometcdf(P,N) = (1 - "probabiity that the first N trials are failures"), or:		However, we can take a shortcut to arrive at a much simpler expression for geometcdf(. Consider the opposite probability to the one we're interested in, the probability that it will '''not''' take "at most N trials", that is, the probability that it will take more than N trials. This means that the first N trials are failures. So geometcdf(P,N) = (1 - "probabiity that the first N trials are failures"), or:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\operatorname{geometcdf}(p,n) = 1-(1-p)^n		\operatorname{geometcdf}(p,n) = 1-(1-p)^n
	~~[[TI-BASIC:~~/math~~\|/math]]~~		</math>

	= Related Commands =		= Related Commands =
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	* [[TI-BASIC:Binompdf\|Binompdf(]]		* [[TI-BASIC:Binompdf\|Binompdf(]]
	* [[TI-BASIC:Binomcdf\|Binomcdf(]]		* [[TI-BASIC:Binomcdf\|Binomcdf(]]
	* [[TI-BASIC:Geometpdf\|Geometpdf(]][[Category:TI-BASIC]]		* [[TI-BASIC:Geometpdf\|Geometpdf(]]
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:02:41Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=GEOMETCDF.GIF
|summary=Calculates the cumulative geometric probability for a single value
|syntax=geometcdf(''probability'', ''trials'')
|location=Press:
# 2ND DISTR to access the distribution menu
# ALPHA E to select geometcdf(, or use arrows.
Press ALPHA F instead of ALPHA E on a TI-84+/SE with OS 2.30 or higher.
|compatibility=TI-83/84/+/SE
|size=2 bytes
}}

This command is used to calculate cumulative geometric probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:
# A specific event has only two outcomes, which we will call "success" and "failure"
# The event is going to keep happening until a success occurs
# Success or failure is determined randomly with the same probability of success each time the event occurs
# We're interested in the probability that it takes '''at most''' a specific amount of trials to get a success.

For example, consider a basketball player that always makes a shot with 1/4 probability. He will keep throwing the ball until he makes a shot. What is the probability that it takes him no more than 4 shots?

# The event here is throwing the ball. A "success", obviously, is making the shot, and a "failure" is missing.
# The event is going to happen until he makes the shot: a success.
# The probability of a success - making a shot - is 1/4
# We're interested in the probability that it takes at most 4 trials to get a success

The syntax here is geometcdf(''probability'', ''trials''). In this case:

:geometcdf(1/4,4

This will give about .684 when you run it, so there's a .684 probability that he'll make a shot within 4 throws.

Note the relationship between [[TI-BASIC:Geometpdf|Geometpdf(]] and geometcdf(. Since geometpdf( is the probability it will take '''exactly''' N trials, we can write that geometcdf(1/4,4) = geometpdf(1/4,1) + geometpdf(1/4,2) + geometpdf(1/4,3) + geometpdf(1/4,4).

= Formulas =

Going off of the relationship between geometpdf( and geometcdf(, we can write a formula for geometcdf( in terms of geometpdf(:

[[TI-BASIC:Math|Math]]
\operatorname{geometcdf}(p,n) = \sum_{i=1}^{n} \operatorname{geometpdf}(p,i) = \sum_{i=1}^{n} p\,(1-p)^{i-1}
[[TI-BASIC:/math|/math]]

(If you're unfamiliar with sigma notation, <math>\sum_{i=1}^{n}</math> just means "add up the following for all values of i from 1 to n")

However, we can take a shortcut to arrive at a much simpler expression for geometcdf(. Consider the opposite probability to the one we're interested in, the probability that it will '''not''' take "at most N trials", that is, the probability that it will take more than N trials. This means that the first N trials are failures. So geometcdf(P,N) = (1 - "probabiity that the first N trials are failures"), or:

[[TI-BASIC:Math|Math]]
\operatorname{geometcdf}(p,n) = 1-(1-p)^n
[[TI-BASIC:/math|/math]]

= Related Commands =

* [[TI-BASIC:Binompdf|Binompdf(]]
* [[TI-BASIC:Binomcdf|Binomcdf(]]
* [[TI-BASIC:Geometpdf|Geometpdf(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Geometcdf - Revision history

KermMartian at 19:11, 24 February 2016

Maintenance script: Initial automated import