2016-10-01

Understand poisson distribution

IntroductionPoisson distribution can be derived from Binomial distribution when $\lim\limits_{n\to\infty}np = \lambda(\lambda\in\mathbb R)$, in which $n$ is the number of trials, $p$ is the probabilit

Math

2016-10-01

Proof of $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$

Theorem: $$c,\ d\in {\bf R},\ \lim_{x\rightarrow \infty} f(x)=c>0,\ \lim_{x\rightarrow \infty} g(x) =d>0$$ then $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$ Proof: Because $y(x)=ln(x)$ i

Math

2016-09-30

Calculate $$\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$$

I came upon the calculation of $\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$ when I was reviewing Poisson distribution. Notice that $\lambda_n = np_n(n\in\mathbb{Z}{\geq 0}, 0\leq p \leq 1)$ and $

Tag: math

Understand poisson distribution

Proof of $$\lim_{x\rightarrow \infty} f(x)^{g(x)} = c^d$$

Calculate $$\lim\limits_{n\to\infty}(1-\frac{\lambda_n}n)^n$$