DistributionIf X∼N(0,1)X \sim N(0,1)X∼N(0,1), then Z=X2∼X2(1)\mathbb{Z} = X^2 \sim \mathcal{X}^2(1)Z=X2∼X2(1) Beta(α\alphaα, β\betaβ) 0<x<10 < x < 10<x<1 Uniform (α\alphaα, β\betaβ) a<x<ba < x < ba<x<b Gamma γ(α,β)\gamma(\alpha, \beta)γ(α,β) f(x)=xα−1Γ(α)θαe−xθf(x) = {x^{\alpha - 1} \over \Gamma(\alpha) \theta^\alpha} e^{-x \over \theta}f(x)=Γ(α)θαxα−1eθ−x Exponential(θ\thetaθ) = γ(α=1,theta)\gamma(\alpha = 1, theta)γ(α=1,theta) Chi-squared(γ\gammaγ) = γ(α=γ2,θ=2)\gamma(\alpha = {\gamma \over 2}, \theta = 2)γ(α=2γ,θ=2) X∼N(μ,σx2)\mathcal{X} \sim N(\mu, \sigma_x^2)X∼N(μ,σx2) → 12πσe−(x−μ)22σx2{1 \over \sqrt{2 \pi} \sigma} e^{-{(x-\mu)^2} \over {2\sigma_x^2}}2πσ1e2σx2−(x−μ)2 Y=g(x)Y=g(x)Y=g(x) fy(y)=∑xkfx(xk)∣dxdy∣@x=xkf_y(y) = \sum\limits_{x_k} f_x(x_k) |{dx \over dy}|_{\text{@} x = x_k}fy(y)=xk∑fx(xk)∣dydx∣@x=xk