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On 5 January 1975, the 12-bit field that had been used for dates in the TOPS-10 operating system for DEC PDP-10 computers overflowed, in a bug known as "DATE75". The field value was calculated by taking the number of years since 1964, multiplying by 12, adding the number of months since January, multiplying by 31, and adding the number of days since the start of the month; putting 2 12 − 1 ...
In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions. It is a crucial step to test the original claim and confirm or reject the accuracy of results as well as for identifying and correcting the flaws in the original experiment. [1]
With M = 365 days in a year, the average number of people required to find a pair with the same birthday is n = 1 + Q(M) ≈ 24.61659, somewhat more than 23, the number required for a 50% chance. In the best case, two people will suffice; at worst, the maximum possible number of M + 1 = 366 people is needed; but on average, only 25 people are ...
The number of the urn that contains his number is the pre-image of that number under the permutation. Hence the prisoners survive if all cycles of the permutation contain at most fifty elements. We have to show that this probability is at least 30%.
In a uniformly-random instance of the stable marriage problem with n men and n women, the average number of stable matchings is asymptotically . [6] In a stable marriage instance chosen to maximize the number of different stable matchings, this number is an exponential function of n . [ 7 ]
There have been a fairly small number of different types of (pseudo-)random number generators used in practice. They can be found in the list of random number generators, and have included: Linear congruential generator and Linear-feedback shift register; Generalized Fibonacci generator; Cryptographic generators; Quadratic congruential generator
Partition the sequence into non-overlapping pairs: if the two elements of the pair are equal (00 or 11), discard it; if the two elements of the pair are unequal (01 or 10), keep the first. This yields a sequence of Bernoulli trials with p = 1 / 2 , {\displaystyle p=1/2,} as, by exchangeability, the odds of a given pair being 01 or 10 are equal.
Assume two particles A and B perform a simple random walk in two dimensions, but they start from different points. The simplest way to couple them is simply to force them to walk together. On every step, if A walks up, so does B, if A moves to the left, so does B, etc. Thus, the difference between the two particles' positions stays fixed.