Difference between independence and correlation – my understanding

Basically, everyone (or almost everyone) knows that independence and correlation equal to zero are different concepts. More importantly, they don’t have two-way relations, which is if you know two random variables X, Y have zero correlation, you cannot imply that X and Y are independent. However, if X and Y are independent, they will be … Continue reading Difference between independence and correlation – my understanding

The Poisson and Exponential Distribution

  (1) Poisson and Exponential Distribution have connections. (2) Poisson distribution is used to describe the number of occurrences per unit of time. (3) While exponential distribution can describe the length of time between each occurrence. (4) Therefore, follow this intuition, if you set Poisson to capture the probability of zero occurrence, we should find the bridge to get … Continue reading The Poisson and Exponential Distribution

Double Mersenne number

From Wikipedia, the free encyclopedia Double Mersenne primes Number of known terms 4 Conjectured number of terms 4 First terms 7, 127, 2147483647 Largest known term 170141183460469231731687303715884105727 OEIS index A077586 In mathematics, a double Mersenne number is a Mersenne number of the form {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p is a prime exponent. Contents  [hide]  1Examples 2Double … Continue reading Double Mersenne number

How a Kalman filter works, in pictures

This is a post from http://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/ which I believe it is the most intuitive explanation of Kalman filter. I have to tell you about the Kalman filter, because what it does is pretty damn amazing. Surprisingly few software engineers and scientists seem to know about it, and that makes me sad because it is such a … Continue reading How a Kalman filter works, in pictures

Bootstrapping and Monte Carlo Simulation

Bootstrapping is resampling from known samples, Monte Carlo is trying to generate data depend on some parameters. We have samples, for example, 3, 2, 1, 5, 6, but sample size is too small, so we resample from this sample set for 10000 times, then the new sample set is more robust to represent something, this … Continue reading Bootstrapping and Monte Carlo Simulation