diff --git a/numpy_questions.py b/numpy_questions.py
index 07a10c1..dd61161 100644
--- a/numpy_questions.py
+++ b/numpy_questions.py
@@ -37,11 +37,16 @@ def max_index(X):
         If the input is not a numpy array or
         if the shape is not 2D.
     """
-    i = 0
-    j = 0
+    if not isinstance(X, np.ndarray):
+        raise ValueError("Input must be a numpy array.")
 
-    # TODO
+    if X.ndim != 2:
+        raise ValueError("Input must be a 2D numpy array.")
 
+    if X.size == 0:
+        raise ValueError("Input array must not be empty.")
+
+    i, j = np.unravel_index(np.argmax(X), X.shape)
     return i, j
 
 
@@ -62,6 +67,7 @@ def wallis_product(n_terms):
     pi : float
         The approximation of order `n_terms` of pi using the Wallis product.
     """
-    # XXX : The n_terms is an int that corresponds to the number of
-    # terms in the product. For example 10000.
-    return 0.
+    pi = 1
+    for i in range(1, n_terms + 1):
+        pi *= (4 * i ** 2) / (4 * i ** 2 - 1)
+    return 2 * pi