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  • 0 posts edited
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Aug
18
accepted Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$
Aug
15
revised Question on sufficient statistics
deleted 2 characters in body
Aug
15
asked Question on sufficient statistics
Aug
15
accepted Calculating a probability mass function (sufficient statistic)
Aug
14
comment Calculating a probability mass function (sufficient statistic)
@AlexR. ahh ok, well that would explain my inconsistent results, thanks.
Aug
14
comment Calculating a probability mass function (sufficient statistic)
@AlexR. so you're saying that $T$ is not a random variable taking values in $1,...,n$ depending on which $X_k$ is the smallest, but instead takes the value of $X_{(1)}$?
Aug
14
asked Calculating a probability mass function (sufficient statistic)
Aug
8
comment Help Proving that $\frac{(1+\frac{1}{t})^t}{e} = 1 -\frac{1}{2t} + O(\frac{1}{t^2})$ for $t\geq 1$
Ansturm is now banned.
Jul
22
accepted Sampling 100 widgets to test for defective ones
Jul
21
comment Sampling 100 widgets to test for defective ones
Yah that's right. I believe their reasoning would have been correct if the $P(B_i)$ were uniform for all $i$, but since $P(B_6)$ is very small compared to $i$'s closer to $50$, their reasoning isn't correct.
Jul
21
comment Sampling 100 widgets to test for defective ones
statistical inference 2nd edition exercise 3.2, the answer isn't actually in the book, I found a (apparently less than perfect) pdf of solutions online.
Jul
21
comment Sampling 100 widgets to test for defective ones
The sampling is done without replacement since I won't be checking the same widget for defectiveness multiple times.
Jul
21
comment Sampling 100 widgets to test for defective ones
@ClementC. the summation can go on to $100$ since as you say once it passes $100-k$ it no longer contributes anything.
Jul
21
comment Sampling 100 widgets to test for defective ones
Yah my formula gives $k=4$ (probably accounting for the fact that $P(B) < 1$), so it's far more in agreement with your estimate. So it looks like my book is in error then, thanks.
Jul
20
revised Sampling 100 widgets to test for defective ones
added 1 characters in body
Jul
20
asked Sampling 100 widgets to test for defective ones
Jul
11
asked Direct construction of an arbitrary elliptic function of order $2$ with pole set contained in its lattice.
Jul
6
accepted Prove that the number of ways to put $n$ distinct balls into $n$ distinct boxes is $n^n$
Jul
6
revised Prove that the number of ways to put $n$ distinct balls into $n$ distinct boxes is $n^n$
added 9 characters in body; edited title
Jul
6
asked Prove that the number of ways to put $n$ distinct balls into $n$ distinct boxes is $n^n$