Suppose that we obtain a bootstrap sample (with n observations) from a population of n observations. (a) What is the probability that the first bootstrap observation is NOT the jth observation from...

Extracted text: Suppose that we obtain a bootstrap sample (with n observations) from a population of n observations. (a) What is the probability that the first bootstrap observation is NOT the jth observation from the original sample? Justify your answer. (b) What is the probability that the second bootstrap observation is NOT the jth observation from the original sample? Justify your answer. (c) What is the probability that the jth observation is in the bootstrap sample? Justify your answer. (d) How will the probability in (b) change when the number of observations increases? Justify your answer. (e) How many different bootstrap samples are there? The order among observations doesn't matter.