diff --git a/AcquistionFunctions/PreferenceExpectedImprovement.py b/AcquistionFunctions/PreferenceExpectedImprovement.py
index b69595c..829b06b 100644
--- a/AcquistionFunctions/PreferenceExpectedImprovement.py
+++ b/AcquistionFunctions/PreferenceExpectedImprovement.py
@@ -22,10 +22,19 @@ class PreferenceExpectedImprovement:
         pass
 
     def rejection_sampling(self):
-        samples = np.empty((self.nr_samples, self.nr_dims))
-        i = 0
-        while i < self.nr_samples:
-            pass
+        samples = np.empty((0, self.nr_dims))
+        while samples.shape[0] < self.nr_samples:
+            # sample from the multi variate gaussian distribution
+            sample = self.rng.multivariate_normal(
+                self.proposal_model_mean, 
+                self.proposal_model_covariance
+            )
+
+            # check if the sample is within the bounds
+            if np.all(sample >= self.lower_bound) and np.all(sample <= self.upper_bound):
+                samples = np.append(samples, [sample], axis=0)
+
+        return samples
 
 
     def expected_improvement(self):