Answer:
The expected number of floors the elevator stops at, not counting the ground floor is =
n*(1-(1-1/n)^m)
Step-by-step explanation:
Here, we want to know the expected number of floors the elevator stops at.
let X1,X2,X3,..Xn are indicator variable for which value =1 if at least one person stops on that floor otherwise value is 0
P(at least one person stops at floor Xj)=1-P(none of m people stops at floor j)
=1-(1-1/n)^m
here total number of floors on elevetor Stops X=X1+X2+X3+...+Xn
hence expected number of floors on elevetor Stops
E(X)=E(X1)+E(X2)+E(X3)...+E(Xn)
=(1-(1-1/n)^m )+(1-(1-1/n)^m )+(1-(1-1/n)^m )+(1-(1-1/n)^m )+..... n times
=n*(1-(1-1/n)^m)
