Statistics for Experimenters - Revision history

Oborn: /* Probability Distributions */

2007-09-20T21:26:07Z

Probability Distributions

Oborn: /* Probability Distributions */

2007-09-20T21:24:24Z

Probability Distributions

Oborn: /* Probability Distributions */

2007-09-20T21:24:08Z

Probability Distributions

Oborn: /* Probability Distributions */

2007-09-20T17:00:19Z

Probability Distributions

Oborn: /* Definitions */

2007-09-10T20:07:05Z

Definitions

Oborn: /* Probability Distributions */

2007-09-06T03:25:29Z

Probability Distributions

Oborn: /* Probability Distributions */

2007-09-05T21:32:02Z

Probability Distributions

Oborn at 16:22, 5 September 2007

2007-09-05T16:22:57Z

Oborn at 16:15, 5 September 2007

2007-09-05T16:15:32Z

New page

;Binomial distribtuion
: best example is a coin toss, its either heads or tails
: mean (<math>\mu</math>) = number of tries <math>n</math>(coin flips) * probability of success<math>p</math> (head, 1/2)
:standard deviation(<math>\sigma</math>) = <math>np(1-p)</math>

; Poisson Distribution
: standard deviation (<math>\sigma</math>) = root of the mean (<math>\sqrt{\mu}</math>)
: use in counting experiments
: the distribtuion approximates the Binomial Distribution for the special case when the mean (<math>\mu</math>) is a lot less than the number of attempts to measure (<math>n</math>) because the probability of the event occurrring is small.
: In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.

;Gaussian/Normal Distribution
: Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) = <math>\Gamma</math>
:standard deviation (<math>\sigma</math>) = <math>\frac{\Gamma} {2.354}</math>
:error = <math>0.675 \sigma</math>

@@ Line 32: / Line 32: @@
 The probability distribution is given as
 :<math>P(k,\mu) = \frac{\mu^{k}e^{-\mu}}{k!}</math>
 ;Gaussian/Normal Distribution

@@ Line 31: / Line 31: @@
 The probability distribution is given as
-:P(k,\mu) = \frac{\mu^{k}e^{-\mu}}{k!}
+:<math>P(k,\mu) = \frac{\mu^{k}e^{-\mu}}{k!}</math>
 ;Gaussian/Normal Distribution

@@ Line 14: / Line 14: @@
 ;Systematic Error
-; Reproducable inaccuracies introduced by faulty equipment, calibration, or technique.
+: Reproducable inaccuracies introduced by faulty equipment, calibration, or technique.
 =Probability Distributions=

← Older revision		Revision as of 16:22, 5 September 2007
Line 1:		Line 1:
		+
		+	= Definitions=
		+
		+	;Accuracy
		+	: A measure of how close the experimental result is to the "true" value
		+
		+	; Precisison
		+	: A meauser of close the result is determined without knowing the true vaule
		+	: Precision is often used to predict the accuracy of a quantity to be measured (you don't know the answer before doing the experiment)
		+
		+
		+	;Random Error
		+	: The error in a result due to the finite precision of an experiment
		+	: A measure of the statistical fluctuations which result after repeated experimentation
		+
		+	;Systematic Error
		+	; Reproducable inaccuracies introduced by faulty equipment, calibration, or technique.
		+
		+
		+	=Probability Distributions=

	;Binomial distribtuion		;Binomial distribtuion

@@ Line 29: / Line 29: @@
 : the distribtuion approximates the Binomial Distribution for the special case when the probability of the event occuring is small.
 : In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.
 ;Gaussian/Normal Distribution

@@ Line 32: / Line 32: @@
 ;Gaussian/Normal Distribution
 : Full WIdth at Half Max (FWHM) = width of the distribution at half the value of the maximum probabilty (distibution peak) = <math>\Gamma</math>
-:standard deviation (<math>\sigma</math>) = <math>\frac{\Gamma} {2.354}</math>
+:standard deviation (<math>\sigma</math>) = <math>\frac{\Gamma} {2 \sqrt{2 \ln 2}} = \frac{\Gamma} {2.354}</math>
 :error = <math>0.675 \sigma</math>

@@ Line 28: / Line 28: @@
 : standard deviation (<math>\sigma</math>) = root of the mean (<math>\sqrt{\mu}</math>)
 : use in counting experiments
-: the distribtuion approximates the Binomial Distribution for the special case when the mean (<math>\mu</math>) is a lot less than the number of attempts to measure (<math>n</math>) because the probability of the event occurrring is small.
+: the distribtuion approximates the Binomial Distribution for the special case when the probability of the event occuring is small.
 : In the cosmic ray telescope experiment the mean number of detected cosmic rays is much smaller than the number of cosmic rays passing by.

@@ Line 1: / Line 1: @@
 = Definitions=
@@ Line 21: / Line 20: @@
 ;Binomial distribtuion
 : best example is a coin toss, its either heads or tails
 : mean (<math>\mu</math>) = number of tries <math>n</math>(coin flips) * probability of success<math>p</math> (head, 1/2)