Continuous
Probability Distributions
Name 
Probability Density Function (pdf), f(x) 
Mean, Variance, Moment Generating Function 
Comments 

Uniform over (a, b) 


¥ ¥ noninformative, randomness distribution 

Gamma parameters 


¥ Very rich family with different shapes 

Exponential parameters 


¥ Gamma with n=1 ¥ (survival function) ¥ memoryless property 

Chisquare parameter 
(nu) is called
the degrees of freedom 

¥ Gamma with 

Beta parameters 


¥ A good model for proportions (Bayesian inference) 

Normal parameters 
Standard Normal m=0,
s=1 

¥ Bell shaped curve ¥ To find a normal probability use the Table 2.3 on page
81 ¥ If has then has ¥ Normal
approximation to binomial. Let X has Binom(n,q). Make the continuity correction and use the fact that 

Bivariate Normal 
Circular normal distribution r=0, s_{1}=s_{2} 
¥ If X and Y have a bivariate normal distribution then 1. Y given X=x has a normal distribution with 2. X given Y=y has a normal distribution with 3. X and Y are independent iff r=0. 
