The SD of a random variable itself being a random variable

Imagine a hierarchical model with 2 random variables of sd0 and sd1 standard deviation. What is the global SD ?

It is simply: SD=sqrt(sd0^2+sd1^2)

sd0 <- 1
sd1 <- 2
x0 <- rnorm(100000, mean=100, sd=sd0)
sd(x0)
var(x0)
x1 <- rnorm(100000, mean=x0, sd=sd1)
sd(x1)
var(x1)
sd0^2+sd1^2
sqrt(sd0^2+sd1^2)

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