How do we get (N-1/N)^x ? And why power of X ? It is given that: number of peopl

Question

How do we get (N-1/N)^x ? And why power of X ? It is given that: number of people who enter an elevator on the ground floor is a Poisson random variable with mean 10. That is, lambda = 10 The probability mass function of the Poisson distribution can be defined as, P(x) = e^-lambda lambda^x/x! Let Y denote the number of people enter the elevator in the first place. Let the variable L_i can be define as, L_i = {1 if the elevator stops the floor 0 otherwise First, find E(sigma^N_i = 1 L | X = x). E(sigma^N_ = 1 L_i | X = x) = sigma^N_ = 1 E [L_i | X = x] = sigma^N_i = 1 P(Someone gets off on floor i | X = x) = sigma^N_i = 1 [1 - P(no one gets off on floor i | X = x] = sigma^N_i = 1 [1 - (N - 1/N)^x] = N[1 - (N - 1/N)^x]

Explanation / Answer

P(one gets of floor I /X=x)=1/N

P(no one gets of floor i/ X=x) = 1-1/N

(N is called total observation)

= (N-1)/N

[(N-1)/N]^x is the add x power observation .so that continues power series .

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