# 5.2

## 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

$(1-1/100)^{100}=0.366$