diff --git a/numpy_questions.py b/numpy_questions.py
index 07a10c1..227ae0d 100644
--- a/numpy_questions.py
+++ b/numpy_questions.py
@@ -15,6 +15,7 @@
 This will be enforced with `flake8`. You can check that there is no flake8
 errors by calling `flake8` at the root of the repo.
 """
+
 import numpy as np
 
 
@@ -41,6 +42,11 @@ def max_index(X):
     j = 0
 
     # TODO
+    if not isinstance(X, np.ndarray):
+        raise ValueError("The input is not numpy array!")
+    if X.ndim != 2:
+        raise ValueError("The input is not a 2D array!")
+    i, j = np.unravel_index(np.argmax(X), X.shape)
 
     return i, j
 
@@ -64,4 +70,13 @@ def wallis_product(n_terms):
     """
     # XXX : The n_terms is an int that corresponds to the number of
     # terms in the product. For example 10000.
-    return 0.
+    if n_terms == 0:
+        return 2.
+
+    product = 1.0
+    for i in range(1, n_terms + 1):
+        numerator = 4 * i ** 2
+        denominator = (4 * i ** 2) - 1
+        product *= numerator / denominator
+
+    return 2 * product