Mathematics, 18.12.2019 21:31 ccamiloggonzales1234

We will now derive the probability that a given observation is part of a bootstrap sample. suppose that we obtain a bootstrap sample from a set of n observations.

a. what is the probability that the first bootstrap observation is not the j^th observation from the original sample? justify your answer.

b. what is the probability that the second bootstrap observation is not the j^th observation from the original sample?

c. argue that the probability that the j^th observation is not in the bootstrap sample is (1 - 1/n)^n.

d. when n = 5, what is the probability that the j^th observation is in the bootstrap sample?

e. when n = 100, what is the probability that the j^th observation is in the bootstrap sample?

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