To solve the problem of finding the probability that at least two persons out of a group of three were born in the same month, we can use the complementary probability approach. Here’s the step-by-step solution:Step 1: Understand the P
For comparison, if probabilistic algorithms are allowed, then by randomly selecting integers between x and 2x to test for primality, it is easy to see from the prime number theorem that one will succeed in obtaining a prime with high probability in time . However, after some effort we were ...
For sake of discussion we normalize the GUE model to be the random Hermitian matrix whose probability density function is proportional to . With this normalization, the famous Wigner semicircle law will tell us that the eigenvalues of this matrix will almost all lie in the interval , and after...
The Poisson probability distribution is a discrete probability distribution that represents the probability of a given number of events happening in a fixed time or space if these cases occur with a known steady rate and individually of the time since the last event. It was titled after French m...
What is the probability that in a group of two people, both will have the same birthday, assuming that there are 365 days in a year and no one has his/her birthday on 29th Fabruary ? View Solution Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives...
Discrete mathematics and probability Abstract Algebra Abstract algebra is one of the divisions in algebra which discovers the truths relating to algebraic systems independent of the specific nature of some operations. These operations, in specific cases, have certain properties. Thus we can conclude some...
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In a time when we find ourselves spending more time together, learning and thinking and playing together at home, I wanted to share a game that is appropriate for players of all ages. The game“Penguins!”is strategic and fun for the whole family!
May I watch TV in the evening? Yes, you may./No, you can’t.May I use your computer? Certainly, Here it is./Sorry, I am using it.May I come in? Yes, please./Come in, please./Please don’t./Wait a moment, please.May I speak to Miss Li, please? Certainly./One moment, ...
8 September, 2024 in math.AP, math.MP | Tags: finite time blowup, incompressible Euler equations | by Terence Tao | 7 comments Given a smooth compact Riemannian manifold , the incompressible Euler equations can be written in abstract index notation as where is a time-dependent scalar field...