Describing the problem - Linear Example

Counting the number of observations of each group of \(X^1\).

same_group_x1_dist_matrix <-
  colSums(same_group_count_matrix) /
  sum(same_group_count_matrix)

round(same_group_x1_dist_matrix, 2)

##   (0,0.2] (0.2,0.4] (0.4,0.6] (0.6,0.8]   (0.8,1] 
##      0.24      0.19      0.16      0.26      0.16