Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the entire sample?
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Luckily, this is just a binomial problem.
To be the smallest, it must be smaller than each of the n-1 previous observations.
For one observation to be smaller than another, the probability is 1/2.
So to be smaller than all n-1, the prob is (1/2)^(n-1)
To be the smallest, it must be smaller than each of the n-1 previous observations.
For one observation to be smaller than another, the probability is 1/2.
So to be smaller than all n-1, the prob is (1/2)^(n-1)