deletions | additions       diff --git a/section_Statistics_The_data_points__.tex b/section_Statistics_The_data_points__.tex  index cd7b370..df29c82 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 et al pair catalogue section.   The data points are grouped 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- a radio detection of one of the two AGN in each quasar pair in the FIRST survey ( referring to a quasar pair as defined by the selection criterion employed by Liu et al 2011) or a failure -not detecting a quasar pair. Liu et al detected 1 286 pairs, i.e we obtained 1286 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 $\frac{1286}{138070} \approx 0.0093$ . We further assume that 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 errors in the projected separations  of our data points are neglected neglected because  the selected  bins width ($\sigma_{rp} << 20 kpc$)  are much larger than theerrors in the  projected separations of our data points, and thus these errors separation uncertainties  (as seen in figure 11 and 12) are approximated by zero. 12).    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  σ^2= np(1-p)