These are the expected numbers of spins that is P(N=n)=n−1/n!
According to the statement
Let N is the number of spins AND
Let S is the sums of spins until the sum is greater than one.
we know that the For N=1, P(S) = 0.
The value of expected random variables are
E(X)=μ=∑xP(x).
Put all the integers values in it and integrate.
According to statement condition the expected number of variables become
P(N=n)=P(Sn−1<1≤Sn)
P(N=n)= P(Sn−1 < 1) - P(Sn <1)
P(N=n)=1/(n−1)!−1/n!
P(N=n)=n−1/n!
So, these are the expected numbers of spins that is P(N=n)=n−1/n!
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