Common distribution of knowledge points for machine learning and data mining

Common distribution of knowledge points for machine learning and data mining Common Distribution (common distribution): Discrete distribution (discrete type distribution): 0-1 distribution (0-1 distribution)
Definition: If a random variable x x only takes 0 0 and 1 12 values, and its distribution law is
P{X=K}=PK (1−p) 1−k,k=0,1 p\{x=k\}=p^k (1-p) ^{1-k}, k=0,1
where x x obeys the (0−1) (0-1) distribution of the parameter P, which is recorded as X∼ (0−1) X \sim (0-1). Toss a coin once and obey the two-point distribution.
The expectation and variance of the two-point distribution are: P,1−p p, 1-p. Geometric distribution (geometric distribution)
Definition: If the possible value of the random variable x x is,... ,... and its distribution law is
p{x=k}= (1−p) k−1p=qk−1p,k=1,2,3,... p\{x=k\}= (1-p) ^{k-1}p=q^{k-1}p, k=1,2,3,...
The random variable x x obeys the geometric distribution of the parameter P and is recorded as X∼g (p) X \sim G (p).
The geometric distribution has no memory, namely:
p{x>m+n| X>m}=p{x>n} p\{x>m+n| X>m\}=p\{x>n\}
The information of the geometric distribution on the past m failures is forgotten in the subsequent calculations.
The geometric distribution corresponds to: x x is an independent repetition of the Bernoulli test, which is the number of trials of "first success".
The expectation and variance of geometric distributions are: 1p,1−pp