diff --git a/Probas.py b/Probas.py
index f4560de..a6879b0 100755
--- a/Probas.py
+++ b/Probas.py
@@ -1,6 +1,6 @@
 #!/usr/bin/python3
 from random import random
-from math import floor, sqrt, factorial
+from math import floor, sqrt, factorial,exp
 from statistics import mean, variance
 from matplotlib import pyplot as plt
 from pylab import *
@@ -61,6 +61,10 @@ def stats_NFBP_iter(R, N):
     Runs R runs of NFBP (for N items) and studies distribution, variance, mean...
     Calculates stats during runtime instead of after to avoid excessive memory usage.
     """
+    Hmean=0
+    Var=[]
+    H=[]
+    Exp=0
     P = R * N  # Total number of items
     print("## Running {} NFBP simulations with {} items".format(R, N))
     # number of bins
@@ -106,17 +110,26 @@ def stats_NFBP_iter(R, N):
     print("Mean number of bins : {} (variance {})".format(I, IVariance), "\n")
     # TODO clarify line below
     print(" {} * {} iterations of T".format(R, N), "\n")
-
-    for n in range(min(N, 10)):
+    for n in range(N):
         Hn = HSum[n] / R  # moyenne
         HVariance = sqrt(HSumVariance[n] / (R - 1) - Hn**2)  # Variance
+        Var.append(HVariance)
+        H.append(Hn)
         print(
             "Index of bin containing the {}th item (H_{}) : {} (variance {})".format(
                 n, n, Hn, HVariance
             )
         )
+    print(HSum)
+    print(len(HSum))
+    for x in range(len(HSum)):
+        Hmean+=HSum[x]
+    Hmean=Hmean/P
+    print("Hmean is : {}".format(Hmean))
+    Exp=np.exp(1)
     HSum = [x / R for x in HSum]
-    # print(HSum)
+    HSumVariance = [x / R for x in HSumVariance]
+    print(HSumVariance)
     # Plotting
     fig = plt.figure()
     # T plot
@@ -176,13 +189,17 @@ def stats_NFBP_iter(R, N):
     cx.set_xlabel("n-item (1-{})".format(N))
     cx.set_title("H histogram for {} items".format(P))
     xb = linspace(0, N, 10)
-    yb = Hn * xb / 10
-    wb = HVariance * xb / 10
-    cx.plot(xb, yb, label="Theoretical E(Hn)", color="brown")
-    cx.plot(xb, wb, label="Theoretical V(Hn)", color="purple")
+    xc=linspace(0,N,50)
+    yb =  [Hmean for n in range(N)]
+    db =(( HSum[30] - HSum[1])/30)*xc
+    wb =(( HSumVariance[30] - HSumVariance[1])/30)*xc
+    cx.plot(xc, yb, label="Experimental Hn_Mean", color="brown")
+    cx.plot(xc, H, label="Experimental E(Hn)", color="red")
+    cx.plot(xc, Var, label="Experimental V(Hn)", color="purple")
     cx.legend(loc="upper left", title="Legend")
-    plt.show()
+   
 
+    plt.show()
 
 def simulate_NFDBP(N):
     """
@@ -219,6 +236,7 @@ def stats_NFDBP(R, N, t_i):
     """
     print("## Running {} NFDBP simulations with {} items".format(R, N))
     # TODO comment this function
+    T1=[]
     P = N * R  # Total number of items
     I = []
     H = [[] for _ in range(N)]  # List of empty lists
@@ -235,6 +253,7 @@ def stats_NFDBP(R, N, t_i):
         for k in range(N):
             T.append(0)
             T = sim["T"]
+            T1.append(sim["T"][0])
         for n in range(N):
             H[n].append(sim["H"][n])
             Tk[n].append(sim["T"][n])
@@ -244,7 +263,7 @@ def stats_NFDBP(R, N, t_i):
     Sum_T = [
         x * 100 / (sum(Sum_T)) for x in Sum_T
     ]  # Pourcentage de la repartition des items
-
+    T1=[x/100 for x in T1]
     print("Mean number of bins : {} (variance {})".format(mean(I), variance(I)))
 
     for n in range(N):
@@ -258,6 +277,7 @@ def stats_NFDBP(R, N, t_i):
     E = 0
     sigma2 = 0
     # print(T_maths)
+    T_maths = [x * 100 for x in T_maths]
     for p in range(len(T_maths)):
         E = E + (p + 1) * T_maths[p]
         sigma2 = ((T_maths[p] - E) ** 2) / (len(T_maths) - 1)
@@ -266,7 +286,7 @@ def stats_NFDBP(R, N, t_i):
             t_i, E, sqrt(sigma2)
         )
     )
-    T_maths = [x * 100 for x in T_maths]
+   # T_maths = [x * 100 for x in T_maths]
     # Plotting
     fig = plt.figure()
     # T plot
@@ -322,8 +342,9 @@ def stats_NFDBP(R, N, t_i):
     bx.legend(loc="upper right", title="Legend")
 
     # Loi mathematique
+    print("ici")
     print(T_maths)
-    cx = fig.add_subplot(224)
+    cx = fig.add_subplot(223)
     cx.bar(
         x,
         T_maths,
@@ -343,6 +364,30 @@ def stats_NFDBP(R, N, t_i):
     cx.set_xlabel("Bins i=(1-{})".format(N))
     cx.set_title("Theoretical T{} values in %".format(t_i))
     cx.legend(loc="upper right", title="Legend")
+   
+    dx = fig.add_subplot(224)
+    dx.hist(
+        T1,
+        bins=10,
+        width=1,
+        label="Empirical values",
+        edgecolor="blue",
+        linewidth=0.7,
+        color="black",
+    )
+    dx.set(
+        xlim=(0, 10),
+        xticks=np.arange(0, 10,1),
+        ylim=(0, 100),
+        yticks=np.linspace(0, 100, 10),
+    )
+    dx.set_ylabel("Number of items in T1 for {} iterations")
+    dx.set_xlabel("{} iterations for T{}".format(R,1))
+    dx.set_title(
+        "T{} items repartition {} items (Number of items in each bin)".format(1, P)
+    )
+    dx.legend(loc="upper right", title="Legend")
+
     plt.show()