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iterations = 100
T_final = 1
j_cells_final = []

for i in range(iterations):
    j = 1
    j_cells = []
    #j_cells.append(j)
    t = 0   
    times = []
    times.append(t)
    while t < T_final:
        t += np.random.exponential(1/j)
        times.append(t)
        j_cells.append(j)
        j +=1    
    j_cells_final.append(j_cells[-1])

print(j_cells_final)

def num_occ(L, n):
    count = 0
    for i in range(len(L)):
        if L[i] == n:
            count +=1
    return count

X = np.amax(j_cells_final)
prob_list = []
for i in range(1,X+1):
    num_occs = num_occ(j_cells_final, i)
    p = num_occs / iterations
    prob_list.append(p)
    #print(i)
print(X)    
print(prob_list)

js = np.linspace(1,X+1,X,endpoint=False)
print(js)

fig, ax = plt.subplots(1, 1, figsize=(9, 6))
plt.plot(js,prob_list)
plt.show()