Simulate the compound random variable S

Let S=X_1+X_2+...+X_N where N is a nonnegative integer-valued random variable and X_1,X_2,... are i.i.d random variables.(If N=0, we set S=0).

Simulate S in the case where N ~ Poi(100) and X_i ~ Exp(0.5). (draw histograms and use the numpy or scipy built-in functions).And check the equations E(S)=E(N)*E(X_1) and Var(S)=E(N)*Var(X_1)+E(X_1)^2 *Var(N)

I was trying to solve it, but I'm not sure yet of everything and also got stuck on the histogram part. Note: I'm new to python or more generally , new to programming.

My work:

import scipy.stats as stats
import matplotlib as plt
N = stats.poisson(100)
X = stats.expon(0.5)
arr = X.rvs(N.rvs())
S = 0
for i in arr:
    S=S+i
print(arr)
print("S=",S)
expected_S = (N.mean())*(X.mean())
variance_S = (N.mean()*X.var()) + (X.mean()*X.mean()*N.var())
print("E(X)=",expected_S)
print("Var(S)=",variance_S)