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Feb 21st, 2020
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- ## a
- The probability that the first observation is not he jth from the original sample is $\frac{n-1}{n}$. There are $n-1$ options that aren't the jth from the original sample, and n total options.
- ## b
- The same as above($\frac{n-1}{n}$), as bootstrapping samples without replacement.
- ## c
- Probability an individual sample is not the jth observation: $\frac{n-1}{n}=(1-\frac{1}{n})$.
- Total number of samples: $n$.
- Thus, the probability that all samples aren't the jth is $(1-1/n)^n$.
- ## d
- $(1-1/5)^5=(4/5)^5=0.32768$
- ## e
- $(1-1/100)^{100}=0.366$

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