Machine Learning formula in LaTex

Bayesian

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

posterior=\frac{likelihood\cdot prior}{constant}

Binomial distribution

P(X=k)=C_n^kp^k(1-p)^{n-k}\\[5pt]n\ is\ the\ total number\ of\ experiments\\ k\ is\ the\ number\ of\ successful\ times\\ p\ is\ the\ probability\ of\ success

Poisson distribution

Poisson distribution is to describe the specific occurrence probability of events in a certain period of time.

P(X=k)=\frac{\lambda^k}{k!}e^{-\lambda},k=0,1,…

P(X=k)=\frac{\lambda^k}{k!}e^{-\lambda},k=0,1,…\\\lambda\ is\ mean,\ k\ is\ times

Exponential distribution

Exponential distribution is a kind of continuous probability distribution, which is used to represent the time interval of independent random events.

f(n)= \begin{cases} \lambda e^{-\lambda x}\quad x>0\\ 0 \quad\quad\quad x\leq0\end{cases}

f(n)= \begin{cases} \lambda e^{-\lambda x}\quad x>0\\ 0 \quad\quad\quad x\leq0\end{cases}

Normal distribution

f(x)=\frac{1}{\sqrt{2\pi}\sigma}e^\frac{(x-\mu)^2}{2\sigma^2}

f(x)=\frac{1}{\sqrt{2\pi}\sigma}e^\frac{(x-\mu)^2}{2\sigma^2}\\\mu\ is\ mean,\ \sigma\ is\ standard\ deviation