Uniform distribution: every datum in range equally likely.

mean=(start+end)/2 ie. midrange

standard deviation= (end-start)/√12 ≈ (end-start)/3.464

skew: 0

Normal/Gaussian distribution: physical quantity that is the sum of many small independent processes.
Also, distribution of sample averages.

mean=median=mode

skew: 0

kurtosis: 0

Binomial distribution: #successes/yeses/ones in n tries when probability of a success is p.

mean= np

standard deviation= √(np(1-p))

skew: (1-2p)/σ

kurtosis: (1-6p(1-p))/σ^{2}

n=1 : **Bernoulli** distribution. p=proportion success

Poisson distribution: λ=expected/average independent #events in an interval.
Probabilities of each k (0-) #occurences/events/arrivals in an interval.

mean= λ

standard deviation= √λ

skew: 1/√λ

kurtosis: 1/√λ

Χ^{2} Chi-squared distribution: sum of k squared standard normals

mean= k

standard deviation= √(2k)

skew:√(8/k)

kurtosis: 12/k ?

Lognormal distribution: its log is normally distributed.
μ and σ are mean and standard deviation of that normal distribution.

mean= *e ^{μ+σ2/2}*

mode=

median=

mode<median<mean

standard deviation=