diff --git a/numpy_questions.py b/numpy_questions.py
index 07a10c1..4a25e25 100644
--- a/numpy_questions.py
+++ b/numpy_questions.py
@@ -41,7 +41,13 @@ def max_index(X):
     j = 0
 
     # TODO
+    if not isinstance(X, np.ndarray):
+        raise ValueError("Input must be a numpy array.")
+    if X.ndim != 2:
+        raise ValueError("Input must be a 2D array.")
 
+    max_idx = np.unravel_index(np.argmax(X), X.shape)
+    i, j = max_idx
     return i, j
 
 
@@ -64,4 +70,12 @@ 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:
+        raise ValueError("Number of terms must be non-negative.")
+
+    product = 1.0
+    for n in range(1, n_terms + 1):
+        term = (4 * n ** 2) / (4 * n ** 2 - 1)
+        product *= term
+
+    return product * 2