Continuous

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

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

Exponential($\lambda$$\lambda$)

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

Gamma($\alpha$$\alpha$,λ)

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

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

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

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

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

Uniform (L,R)

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