diff --git a/tests/link/jax/test_random.py b/tests/link/jax/test_random.py
index ade208754d..e8ecc42d05 100644
--- a/tests/link/jax/test_random.py
+++ b/tests/link/jax/test_random.py
@@ -600,12 +600,10 @@ def test_random_concrete_shape_subtensor_tuple():
     assert jax_fn(np.ones((2, 3))).shape == (2,)
 
 
-@pytest.mark.xfail(
-    reason="`size_at` should be specified as a static argument", strict=True
-)
 def test_random_concrete_shape_graph_input():
+    """JAX cannot JIT-compile random variables whose `size` argument is not static."""
     rng = shared(np.random.RandomState(123))
     size_at = at.scalar()
     out = at.random.normal(0, 1, size=size_at, rng=rng)
-    jax_fn = function([size_at], out, mode=jax_mode)
-    assert jax_fn(10).shape == (10,)
+    with pytest.raises(NotImplementedError, match=r".* concrete values .*"):
+        function([size_at], out, mode=jax_mode)