Common Probability Distributions

Common Probability Distributions

Continuous Uniform Distribution:

Binomial distribution

●　E(X)=np

●　D(X)=np(1-p)

Poisson Distribution

●　E(X)=λ

●　D(X)=λ

Normal Distribution:

●　Completely described by mean and variance (μ,σ2).

●　It is symmetric with skewness measure of 0,i.e.,mean=mode=median.(https://www.daowen.com)

●　Kurtosis=3.

●　Linear combinations of normal random variables are normally distributed.

●　Standardized Normal Distribution

●　Confidence Interval

68% of observations fall within±1σ.

90% of observations fall within±1.65σ.

95% of observations fall within±1.96σ.

99% of observations fall within±2.58σ.

Student's t-distribution:

●　Student's t-distribution:is symmetric;fatter tails;

●　Degrees of freedom=(n-1).