diff --git a/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java b/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java
index c2323fc48..f5c920b61 100644
--- a/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java
+++ b/src/main/java/org/apache/commons/math3/random/EmpiricalDistribution.java
@@ -637,7 +637,11 @@ public class EmpiricalDistribution extends AbstractRealDistribution {
         final double pB = pB(binIndex);
         final RealDistribution kernel = k(x);
         if (kernel instanceof ConstantRealDistribution) {
-            return pBminus + pB;
+            if (x < kernel.getNumericalMean()) {
+                return pBminus;
+            } else {
+                return pBminus + pB;
+            }
         }
         final double[] binBounds = getUpperBounds();
         final double kB = kB(binIndex);
diff --git a/src/test/java/org/apache/commons/math3/random/EmpiricalDistributionTest.java b/src/test/java/org/apache/commons/math3/random/EmpiricalDistributionTest.java
index abc96f263..23dd34618 100644
--- a/src/test/java/org/apache/commons/math3/random/EmpiricalDistributionTest.java
+++ b/src/test/java/org/apache/commons/math3/random/EmpiricalDistributionTest.java
@@ -448,7 +448,7 @@ public final class EmpiricalDistributionTest extends RealDistributionAbstractTes
         Assert.assertEquals(0.5, dist.cumulativeProbability(0), Double.MIN_VALUE);
         Assert.assertEquals(1.0, dist.cumulativeProbability(1), Double.MIN_VALUE);
         Assert.assertEquals(0.5, dist.cumulativeProbability(0.5), Double.MIN_VALUE);
-        Assert.assertEquals(1.0, dist.cumulativeProbability(0.7), Double.MIN_VALUE);
+        Assert.assertEquals(0.5, dist.cumulativeProbability(0.7), Double.MIN_VALUE);
     }   
     
     /**
@@ -488,11 +488,11 @@ public final class EmpiricalDistributionTest extends RealDistributionAbstractTes
             Assert.assertTrue(Arrays.binarySearch(values, dist.sample()) >= 0);
         }
         final double tol = 10E-12;
-        Assert.assertEquals(0.2, dist.cumulativeProbability(1), tol);
+        Assert.assertEquals(0.0, dist.cumulativeProbability(1), tol);
         Assert.assertEquals(0.2, dist.cumulativeProbability(2), tol);
-        Assert.assertEquals(0.8, dist.cumulativeProbability(10), tol);
+        Assert.assertEquals(0.6, dist.cumulativeProbability(10), tol);
         Assert.assertEquals(0.8, dist.cumulativeProbability(12), tol);
-        Assert.assertEquals(1.0, dist.cumulativeProbability(13), tol);
+        Assert.assertEquals(0.8, dist.cumulativeProbability(13), tol);
         Assert.assertEquals(1.0, dist.cumulativeProbability(15), tol);
 
         Assert.assertEquals(2.0, dist.inverseCumulativeProbability(0.1), tol);