News
June 27, 2018
Congratulations to Mirza Uzair Baig at the University of Hawai’i at Mānoa, who wrote an excellent solution to the problem.
Note that the statistic Tn may be represented as
\[ T_n = I_{Y_{(1)} < X_{(1)}, Y_{(n)} < X_{(n)}}\, \bigg [\sum_{i = 1}^n
I_{Y_i < X_{(1)}} + \sum_{i = 1}^n I_{X_i > Y_{(n)}}\bigg ]\]
\[+ \,I_{X_{(1)} < Y_{(1)}, X_{(n)} < Y_{(n)}}\, \bigg [\sum_{
i = 1}^n I_{X_i < Y_{(1)}} + \sum_{i = 1}^n I_{Y_i > X_{(n)}}\bigg ].\]
Denote the empirical CDF of $X_1, \cdots , X_n$ by $F_n$…
Deadline: September 7, 2018
Here’s Anirban DasGupta’s latest puzzle, probability this time:
This problem is a comparatively simple one. You can get a reasonable idea of the answers to the questions that we pose by large simulations, but you cannot get the algebraic answers that we are asking for. Here…
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MATRIX is offering fully-funded 1–4 week programs (catering and accommodation)…