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I received this question for a Statistics / Machine Learning assignment and I'd like to you if any of you know the proper answer.

If we have n data points, what is the probability that a given data point does not appear in a bootstrap sample?

Sounds simple enough right? I'm reading Introduction to Statistical Learning to try and find the solution but I would definitely appreciate some help

  • This question appears to be off-topic because it is about statistics and has been flagged for migration to Cross Validated. – Thomas Mar 03 '14 at 09:41

2 Answers2

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Well, the probability of something not happening in n trials is something like (1 - P1)^n where P1 is the probability for one trial. What is the probability of selecting a given value? If you substitute that, does it look like an equation you know involving Euler's number e ??

Robert Dodier
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  • I don't know what the probability is of finding a given datapoint from n in a bootstrap sample, we are not given any numerical values in this question. I believe it is simply 1 trial with n datapoints, but I do not know how to find the probability that one of those n datapoints will be in the bootstrap sample. I believe the formula for this pertains directly to the way Bootstrap sampling works, but I can't seem to figure it out from other formulas for Bootstrapping. –  Mar 03 '14 at 01:13
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the probability for one trial with n data points is 1/n. hence the equation looks like (1-1/n)**n