Workshop:  Background Radiation

STUDENT #1 NAME:                                                                

STUDENT #2 NAME:

Fill in the table below with your background radiation data (you should have 50 X's in the table):

({{   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, {   ,    ,    ,    ,    ,    ,    ,    ,    ,    ,    }, { 0  ,  1  ,  2  ,  3  ,  4  ,  5  ,  6  ,  7  ,  8  ,  9  ,  10  }})

1. Calculate the average number of counts,  \(TraditionalForm\`n\&_\) using the data in the above table.  Do your calculation explicitly using Mathematica.

\(\(\(\ \ \)\(n\&_ = \ \(\(n\_\(\(\ \)\(1\)\) + n\_\(\(\ \)\(2\)\)\  + n\_\(\(\ \)\(3\)\(\ \)\) + n\_\(\(\ \)\(4\)\(\ \)\) + n\_\(\(\ \)\(5\)\(\ \)\) + n\_\(\(\ \)\(6\)\(\ \)\) + \ \ \ \(+n\_\(\(\ \)\(N\)\(\ \)\)\)\)\/N = \ \(∑\+\(α = 1\)\%Nn\( \(n\)\(\ \)\)\_\(\(α\)\(\ \)\)\)\/N\)\)\)\)

2.Calculate the standard deviation using the above data.

\(\(\(\ \ \ \)\(σ = \ \@\(\(\(\((n\_\(\(\ \)\(1\)\) - n\&_)\)\^2 + \((n\_\(\(\ \)\(2\)\) - n\&_)\)\^2\  + \((n\_\(\(\ \)\(3\)\) - n\&_)\)\^2 + \((n\_\(\(\ \)\(4\)\) - n\&_)\)\^2 +  ... \)\ \ \  + \((n\_\(\(\ \)\(N\)\) - n\&_)\)\^2\)\/N\)\)\)\)

3. Convert the data in the above table into a probability distribution P[n].  You may use the EXAMPLE below to make a histogram of you probability distribution.

<< "Graphics`Graphics`"
data = {{0, 22}, {1, 23}, {2, 25}, {3, 26}, {0, 27}, {1, 
            28}};
BarChart[data]

4. Calculate the average number of counts, \(TraditionalForm\`n\&_\) using P[n] from problem #3 above and the formula

\(\(\(\ \ \)\(n\&_ = \ ∑\+\(n = 0\)\%∞ 
          n\ P[n]\)\)\)

Does your answer agree with the answer you gave in problem #1?  Why or why not?

5.Calculate the standard deviation using the above data.

\(\(\(\ \ \ \)\(σ = \ \@\(∑\+\(n = 0\)\%∞\((n - n\&_)\)\^2\ P[n]\)\)\)\)

Does your answer agree with the answer you gave in problem #2?  Why or why not?