deletions | additions       diff --git a/section_Statistics_The_data_points__.tex b/section_Statistics_The_data_points__.tex  index b92a1f9..82679e8 100644  --- a/section_Statistics_The_data_points__.tex  +++ b/section_Statistics_The_data_points__.tex 
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The data points (quasar pairs) collected for our study offers us the biggest sample space possible, as it was obtained from the biggest spectroscopy survey – the SDSS. Our sample has been created through the use of the criteria in the Liu pair catalogue section.   The data points are put into bins. This study makes use of binomial statistics for data analysis purposes.  The data points – the quasar pairs- follow a binomial distribution where the event of detecting a quasar that is in a quasar pair denotes a success. We have 138 070 Bernoulli trials. Where each trial either results in a success- detecting a quasaur pair in the FIRST survey ( referring to a quasar pair as defined by the selection criterion employed by Liu et all al  2011) or a failure -not detecting a quasar pair. Liu et al detected 1 286 pairs, i.e we obtained 2 572 successes. n= 138 070, is the number of trials we conduct or the total number of AGN we have available. The probability of a success is 2572/138070≈ 0.0186 $\frac{2572}{138070} \approx 0.0186$  . We further assume that thek the  trial are independent from each other (under the guidance of our selection criteria). Our variable of interest is the number of successes observed during the n trials. There are about 200 pairs per projected separation bin and the bins are randomly cut to be a similar size. The sample space is cut into 6 bins. The sizes of the bins are much larger than the errors in the projected separations of our data points, and thus these errors (as seen in figure 11 and 12) are approximated by zero.    For figure 11 we plotted the binned averages of radio luminosity with separation. Using the binomial theorem each of the y-error bars is calculated using