TF ErrAna Homework - Revision history

Foretony: /* Gaussian Probability */

2020-02-19T21:47:38Z

Gaussian Probability

2018-03-30T21:10:33Z

Matrix Inversion

2016-03-08T22:59:42Z

2 Eq. 2 unknowns

2016-02-05T22:24:38Z

Histograms by Hand

2016-02-02T23:05:28Z

Electron radius

2016-01-29T01:19:08Z

Find 3 published examples of data which is wrongly represented.

2015-05-10T20:05:16Z

Linear Data Fit

2015-04-02T22:47:15Z

Counting experiment variance

2014-04-18T20:39:37Z

Linear Data Fit

2014-03-21T19:08:48Z

3 Eq. 3 unknowns

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 == Gaussian Probability==
 a.) Determine, by direct integration, the probability  of observing a value beyond 1 standard deviation from the mean of a Gaussian distribution? ie: <math>P_G(X \le \mu - \sigma, \mu, \sigma)+ P_G(X \ge \mu + \sigma, \mu, \sigma)</math> =?
 b.) Find the value of <math>A</math> such that <math>P_G(\mu + \sigma, \mu, \sigma) = A P_G(\mu,\mu,\sigma)</math>.

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 ==Matrix Inversion==
-Use the Gauss-Jordan method to find the inverse matrix <math>\tilde{A}^{-1}</math> given
+Use the Gauss-Jordan method to find the inverse matrix <math>\tilde{A}^{-1}</math>  '''by hand''' given
 :<math> \tilde{A} =

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 ==2 Eq. 2 unknowns==
-Determine <math>x</math> & <math>y</math> for the system below
+Determine <math>x</math> & <math>y</math> for the system below using either Kramer's Rule or Matrix inversion
 :<math>7x + 8y =100</math>

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 a.) calculate the mean and standard deviation
-b.) construct a histogram by hand which has 10 bins centered on 10,20,...
+b.) construct a histogram by hand which has 10 bins from 0 to 100 and centered on 10,20,...
 c.) Use ROOT to construct a histogram.  Compare the mean and RMS from ROOT with your result in part (a) above.  What is the difference between the RMS report in the ROOT histogram and the standard deviation you calculated in part (a)?

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 :<math>P(r) = Cr^2 \exp^{-2 \frac{r}{R}}</math>
-Doing the integrals by hand (no tables) ,
+Doing the integrals by hand (no tables or software that performs integrals) ,
 a.)Find the value of C

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 ==Find 3 published examples of data which is wrongly represented.  ==
-Identify what is incorrect about it.  What does it mean to be wrongly presented?  A typical example is a political poll which does not identify the statistical uncertainty properly or at all.
+hand in a copy of the example.  Identify what is incorrect about it.  What does it mean to be wrongly presented?  A typical example is a political poll which does not identify the statistical uncertainty properly or at all.
 ==Create a Histogram using ROOT==

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 {| border="1"  |cellpadding="20" cellspacing="0
 |-
-| Trial || Posiiton (cm) ||Temperature (Celsius)
+| Trial || Position (cm) ||Temperature (Celsius)
 |-
 |1 ||1.0||15.6

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 == Counting experiment variance==
-a.)What is the standard deviation for a counting experiment with a mean <math>\mu</math> = 100.
+a.)What is the standard deviation for a counting experiment with a mean number of counts <math>\mu</math> = 100.
-b.)What is the standard deviation if the mean number of counts is increased by a factor of 4?
+b.)What is the standard deviation if you repeat the above counting experiment ten times?
 == Half Width -vs- variance==

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 |}
-a.) Fit the above data assuming a linear function
+a.) Using the program developed in Lab 10, fit the above data assuming a linear function
 T = A + B X

← Older revision		Revision as of 19:08, 21 March 2014
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−	a.)Express a the solution for X,Y, and Z in matrix form assuming the remaining terms in the above are known (<math>A,B,C</math> and <math>a_{ij}</math> are known)	+	a.)Express a the solution for x,y, and z in matrix form assuming the remaining terms in the above are known (<math>A,B,C</math> and <math>a_{ij}</math> are known)