probability density histogram with Matplotlib doesnt make sense

Question

I have just run a simple task of trying to plot the probability density histogram for a simulation I ran. However, when I plot it, the probability for each bin seems not to match the result of the frequency plot. with 50 bins i would expect each bin to have an average probability of 2% which is not reflected in the chart.

Thanks in advance

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

plntAcres = 88.0
hvstPer = 0.99
hvstAcres = plntAcres*hvstPer
yldAcre = np.random.triangular(47,48,49, 10000)

carryIn = 464
pdn = hvstAcres * yldAcre
imp = 25.0
ttlSup = carryIn + pdn + imp

crush = np.random.uniform(1945, 1990,10000)
expts = np.random.uniform(2085, 2200,10000)
seedRes = 130
ttlDem = crush + expts + seedRes

carryOut = ttlSup - ttlDem

print carryOut

plt.hist(carryOut, bins=50,normed=True)
plt.title("Carry Out Distribution")
plt.xlabel("Value")
plt.ylabel("Probability")
plt.show()

Probability density of Carry out

Answer 1

In the hist function, the normed argument does not result in probabilites, but in probability densities. If you want the probabilities themselves, use the weights argument instead (and supply with 1 / len(carryOut)).

The crucial two lines:

weights = np.ones_like(carryOut) / (len(carryOut))
plt.hist(carryOut, bins=50, weights=weights)