> #4A
> B = seq(100,100000, by=1)
> #B
> prior = rep(1/length(B), length(B))
> #C
> length(prior)
[1] 99901
> #100<=B<=1000
> sum(prior[1:901])
[1] 0.009018929
> #1000<=B<=10000
> sum(prior[901:9901])
[1] 0.0900992
> #10000<=B<=100000
> sum(prior[9901:99901])
[1] 0.9009019
> #D
> loguniformprior=1/B
> loguniformprior = loguniformprior/sum(loguniformprior)
> #E
> # 100<=B<=1000
> sum(loguniformprior[1:901])
[1] 0.3338884
> #1000<=B<=10000
> sum(loguniformprior[901:9901])
[1] 0.3331712
> #10000<=B<=100000
> sum(loguniformprior[9901:99901])
[1] 0.3330995
> #F
> #EV
> sum(B*loguniformprior)
[1] 14451.66
> #SD
> sqrt(sum((B^2)*prior2)-sum(B*prior2))
[1] 26894.07