# Continuous

### Chi-squared, ${\displaystyle \chi ^{2}}$(${\displaystyle \alpha }$)

• Mean: ${\displaystyle a}$
• Variance: ${\displaystyle 2a}$
• Density function: ${\displaystyle f(x)=2^{-\alpha /2}(\Gamma (\alpha /2))^{-1}x^{(\alpha /2){-1}}e^{-x/2}}$

### Exponential(${\displaystyle \lambda }$)

• Mean: ${\displaystyle {\lambda ^{-1}}}$
• Variance: ${\displaystyle {\lambda ^{-2}}}$
• Density function: ${\displaystyle f(x)=\lambda {e}^{-\lambda {x}}}$

### Gamma(${\displaystyle \alpha }$,λ)

• Mean: ${\displaystyle \alpha \over \lambda }$
• Variance:${\displaystyle \alpha \over {\lambda ^{2}}}$
• Density function: ${\displaystyle f(x)={\lambda ^{\alpha }{x}^{\alpha {-1}} \over \Gamma (\alpha )}{e}^{-\lambda {x}}}$

### Lognormal(${\displaystyle \mu }$,${\displaystyle \sigma ^{2}}$)

• Mean: ${\displaystyle exp(\mu +{{\sigma ^{2}}/2})}$
• Variance: ${\displaystyle exp(2\mu +\sigma ^{2})(exp(\sigma ^{2})-1)}$
• Density function:${\displaystyle f(x)=(2\pi \sigma ^{2})^{-1/2}x^{-1}exp({-({1}/{2\sigma ^{2}})}(lnx-\mu )^{2})}$

### N(${\displaystyle \mu }$,${\displaystyle \sigma ^{2}}$)

• Mean: ${\displaystyle \mu }$
• Variance: ${\displaystyle \sigma ^{2}}$
• Density function: ${\displaystyle f(x)=(2\pi \sigma ^{2})^{-1/2}exp({-({1}/{2\sigma ^{2}})}(x-\mu )^{2})}$

### Uniform (L,R)

• Mean: ${\displaystyle {L+R} \over 2}$
• Variance:${\displaystyle {(R-L)^{2}} \over {12}}$
• Density function: ${\displaystyle f(x)={{1} \over {(R-L)}}}$