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 Sord= (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.
(In reply to re: reconcider c
) 38/7 ~= 5.4285714285714285713
b) 228/7 ~= 32.5714285714285714285 (these two add up to 38)
c) 36/37 ~= 0.9729729729729729729
All the above is ok. 5.43 & 32.57 are symmetrical vs midrange number i.e. 18.5 (= equidistant from the 1st and last numbers) and indeed sum-up to 38.
@Ch & St .- sorry
My erroneous interpretation (looking at c as if it equalled 97%) was made on a bad day. My answers were 5.43 & 32.57 for a. and b, plus "less than one " for c.
Somehow I misunderstood your results , which were absolutely correct.