Let us denote by S the set of 6 integers (their inclusive range being 1 to 37) drawn at random in a weekly lottery.

Given S_ord= (m₁, m₂ ,m₃ ,m₄, m₅, m₆ ) , where the said integers are placed in increasing order, please answer the following questions:

a) What is the expected value of m₁?
b) What is the expected value of m₆?
c) If your "guess set" consists of 6 distinct integers, chosen randomly within the defined range, what is the expected quantity of numbers in this set that match the drawing's results?

Please resolve analytically and then compare your answers with the results of a simulation, based on at least 100,000 independent drawings.