diff --git a/src/System/Random/Effect.hs b/src/System/Random/Effect.hs
--- a/src/System/Random/Effect.hs
+++ b/src/System/Random/Effect.hs
@@ -102,7 +102,7 @@
                -> Eff (State Random :> r) w
                -> Eff r w
 runRandomState seed computation =
-  fmap snd (runState seed computation)
+  snd <$> runState seed computation
 {-# INLINE runRandomState #-}
 
 -- | A generalized form of generating a random number of the correct type
@@ -205,10 +205,7 @@
 --
 --   Returns a number in the inclusive range [0, range].
 --
---   'hMask' is the mask to get the number of bits per random number
---   we generate.
---
---   'nBits' is the number of bits in 'range'.
+--   'numBits' is the number of bits in 'range'.
 uniformIntDist' :: Member (State Random) r
                 => Integer -- ^ range
                 -> Int     -- ^ numBits
@@ -300,8 +297,6 @@
 --
 --   t must be >= 0
 --   p must be in the range [0, 1].
---
---   Warning: NOT IMPLEMENTED!
 binomialDist :: Member (State Random) r
              => Int  -- ^ t
              -> Rational -- ^ p
@@ -315,9 +310,8 @@
     trials <- V.replicateM t randomDouble
 
     let p'           = realToFrac p
-        succeeded    = V.map (<= p') trials
         numSuccesses =
-          V.foldl' (\s b -> if b then s+1 else s) 0 succeeded
+          V.foldl' (\s x -> if x <= p' then s+1 else s) 0 trials
 
     return numSuccesses
 
@@ -489,11 +483,12 @@
 
 -- | Performs O(n) work building a table which we can later use
 --   sample with 'discreteDist'.
-buildDDH :: [Integer] -> DiscreteDistributionHelper
+buildDDH :: [Word64] -> DiscreteDistributionHelper
 buildDDH xs =
-  let vs = V.fromList xs
-      s  = V.sum vs
-      ns = V.map (% s) vs -- normalize the list
+  let vs  = V.fromList xs
+      s   = fromIntegral (V.sum vs)
+      vs' = V.map fromIntegral vs
+      ns  = V.map (% s) vs' -- normalize the list
    in DDH (V.postscanl' (+) 0 ns)
 
 -- | Given a pre-build 'DiscreteDistributionHelper' (use 'buildDDH'),
@@ -510,7 +505,7 @@
 discreteDist (DDH xs) = do
   y <- realToFrac <$> randomDouble
   return $ runST $ do
-    mv <- V.thaw xs
+    mv <- V.unsafeThaw xs
     binarySearch mv y
 
 -- | This function produces random floating-point numbers, which
diff --git a/system-random-effect.cabal b/system-random-effect.cabal
--- a/system-random-effect.cabal
+++ b/system-random-effect.cabal
@@ -1,5 +1,5 @@
 name:                system-random-effect
-version:             0.1.2.0
+version:             0.2.0
 synopsis:            Random number generation for extensible effects.
 homepage:            https://github.com/wowus/system-random-effect
 license:             BSD3
diff --git a/test/Test.hs b/test/Test.hs
--- a/test/Test.hs
+++ b/test/Test.hs
@@ -3,6 +3,7 @@
 module Main ( main ) where
 
 import Control.Eff
+import Control.Eff.State
 
 import System.Random.Effect
 
@@ -20,6 +21,9 @@
 main :: IO ()
 main = defaultMain tests
 
+runWithSeed :: Word64 -> Eff (State Random :> ()) a -> a
+runWithSeed seed = run . runRandomState (mkRandom seed)
+
 checkRange :: (Integer, Integer) -> Integer -> Bool
 checkRange (low, high) x =
   x >= low && x <= high
@@ -29,9 +33,29 @@
   let low  = min a b
       high = max a b
 
-   in checkRange (low, high) $ run $ runRandomState (mkRandom seed) $ do
+   in checkRange (low, high) . runWithSeed seed $ do
         uniformIntDist a b
 
+testDiscreteDistributionInRange :: [Word64] -> Word64 -> Bool
+testDiscreteDistributionInRange xs seed =
+  let ddh = buildDDH xs
+      minVal = 0
+      maxVal = length xs - 1
+   in length xs == 0 || sum xs == 0 ||
+        ((\x -> x >= minVal && x <= maxVal) . runWithSeed seed $
+          discreteDist ddh)
+
+testNoZeroDiscreteDistributionPick :: [Word64] -> Word64 -> Bool
+testNoZeroDiscreteDistributionPick xs seed =
+  let ddh = buildDDH xs
+      minVal = 0
+      maxVal = length xs - 1
+   in length xs == 0 || sum xs == 0 ||
+        ((\x -> (xs !! x) /= 0) . runWithSeed seed $
+          discreteDist ddh)
+
 tests =
   [ testProperty "random range" testUniformRandom
+  , testProperty "discrete dist range" testDiscreteDistributionInRange
+  , testProperty "no non-zero discrete dist pick" testNoZeroDiscreteDistributionPick
   ]