added script for first passage time of random walker

statistics/exercises/randomwalkfirstpassagetime.py

@@ -0,0 +1,34 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+# first passage time of random walker
+# the average of the first passage time grows
+# the more experiments you average (n)
+# eventually diverges to infinity
+# see https://www.math.ucdavis.edu/~tracy/courses/math135A/UsefullCourseMaterial/firstPassage.pdf last paragraph
+
+p = 0.5
+thresh = 1.0
+rep = 1
+rn = 10000
+n = 2
+meantimes = np.zeros(rep)
+for i in range(rep):
+    times = np.zeros(n)
+    for k in  range(n):
+        xx = 0.0
+        xxinx = 0
+        while True:
+            r = np.random.rand(rn)
+            x = np.zeros(len(r))
+            x[r < p] = 1.0
+            x[r >= p]= -1.0
+            y = xx + np.cumsum(x)
+            inx = np.where(y > thresh)[0]
+            if len(inx) > 0:
+                times[k] = xxinx + inx[0]
+                break
+            xx = y[-1]
+            xxinx += len(x)
+    meantimes[i] = np.mean(times)
+print np.mean(meantimes)