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Answer:
Hence the person stop at floor by at least one person will be
E(X)=(summation from K=1 to k)[1-{(k-1)/k}^n]
Step-by-step explanation:
Given:
There are n peoples and k floors in a building.
Selects floor with 1/k probability .
To find :
Elevator stop at each floor by at least one person.
Solution:
Now
let K= number of floor at which at least one person will be stopping.
For getting E(X)
consider a variable Ak =1 if a least one person get of the elevator
and values for k=1,2,3.....k
K=(summation From k=1 to k)Ak
E(K)=((summation From k=1 to k) E[Ak]
=(summation From k=1 to k)[
Hence the person stop at floor by at least one person will be
E(K)=(summation from K=1 to k)[1-{(k-1)/k}^n]