# 2021.12.16
# AmirHosein Sadeghimanesh
# 
# The goal is to apply Lemma 5.2 of the superlevel set paper to conclude
# that with probability one, the rectangle [2, 2.5] * [2.5, 3] in Figure
# 3c of the Kac-Rice paper (the arXiv version) which has average number
# of solutions equal to 2 is not a rectangle that almost all of it is
# inside the region with 2 solutions, but instead has non-zero measure 
# intersections with regions of different number of solutions.
#
Task: MCKR integrate
Save_location: ./
Save_name: File_20211216_testing_Lemma_5_2_output_2
MCKR_file_name: Kac_Rice_Example_2_3_normal
Box: [2,2.5,2.25,0.1],[2,3,2.5,0.1]
MC_method: Antithetic
Sample_size: 10^9
Include standard error
Include integration time
Include cpu information
Include memory information