1. 高斯分布 pdf = 1/√2\phi \thea exp(-(x-u)^2/2\thea^2)
2. x1 ~ N(u1,v1) x2 ~ N(u2,v2)
E(x1 + x2) = u1 + u2
Var(x1 + x2) = E((x1+x2)^2) - E(x1+x2)^2
= E(x1^2) + E(x2^2) + 2E(x1x2) - E(x1)^2 - 2E(x1)E(x2) - E(x2)^2
= Var(x1) + Var(x2) + 2(E(x1x2) - E(x1)E(x2))
= Var(x1) + Var(x2) + 2cov(x1,x2)
当x1 x2 jointly norm 分布时,cov(x1,x2) = 0
3. pdf 不能直接相加求和
时间: 2024-10-29 22:51:52