diff --git a/hw2/hw2_10.png b/hw2/hw2_10.png
new file mode 100644
index 0000000..72c739e
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diff --git a/hw2/hw2_10.py b/hw2/hw2_10.py
new file mode 100644
index 0000000..cb28e7b
--- /dev/null
+++ b/hw2/hw2_10.py
@@ -0,0 +1,54 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def generate_data(length, noise_prob):
+    x = np.random.uniform(-1, 1, (length, ))
+    x = np.sort(x)
+    y = np.sign(x)
+    noise_mask = ( np.random.rand(length) <= noise_prob  )
+    y[noise_mask] *= -1
+    return x, y
+
+def decision_stump(x, y):
+    theta_seq = np.array([-1] + [(x[i]+x[i+1])/2 for i in range(x.shape[0]-1)])
+    
+    best_Ein = 1e9
+    theta_ans = 0
+    sign_ans = 0
+
+    for theta in theta_seq:
+        Ein = [0, 0]
+        for s in [1, -1]:
+            h_of_x = s * np.sign(x-np.array([theta]*x.shape[0]))
+            index = 0 if s == 1 else 1
+            Ein[index] = (h_of_x != y).sum()
+        
+        if min(Ein) < best_Ein:
+            best_Ein = min(Ein)
+            if Ein[0] < Ein[1]:
+                sign_ans = 1
+                theta_ans = theta
+            else:
+                sign_ans = -1
+                theta_ans = theta
+
+    return best_Ein/x.shape[0], theta_ans, sign_ans
+            
+Ein_log, Eout_log = [], []
+for i in range(2000):
+    x, y = generate_data(32, 0.1)
+    # print(x, y)
+    Ein, theta, sign = decision_stump(x, y)
+    # print(Ein, theta, sign)
+    Ein_log.append(Ein)
+    Eout_log.append(0.5-0.4*sign+0.4*sign*abs(theta))
+
+gap = sorted([ Eout_log[i]-Ein_log[i] for i in range(2000) ])
+median = (gap[999]+gap[1000])/2
+
+plt.scatter(Ein_log, Eout_log)
+plt.xlabel("Ein")
+plt.ylabel("Eout")
+plt.title("median: {}".format(median))
+plt.savefig("hw2_10.png")
+plt.show()
diff --git a/hw2/hw2_11.png b/hw2/hw2_11.png
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index 0000000..81c118b
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diff --git a/hw2/hw2_11.py b/hw2/hw2_11.py
new file mode 100644
index 0000000..ba1c5c7
--- /dev/null
+++ b/hw2/hw2_11.py
@@ -0,0 +1,55 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def generate_data(length, noise_prob):
+    x = np.random.uniform(-1, 1, (length, ))
+    x = np.sort(x)
+    y = np.sign(x)
+    noise_mask = ( np.random.rand(length) <= noise_prob  )
+    y[noise_mask] *= -1
+    return x, y
+
+def decision_stump(x, y):
+    theta_seq = np.array([-1] + [(x[i]+x[i+1])/2 for i in range(x.shape[0]-1)])
+    
+    best_Ein = 1e9
+    theta_ans = 0
+    sign_ans = 0
+
+    for theta in theta_seq:
+        Ein = [0, 0]
+        for s in [1, -1]:
+            h_of_x = s * np.sign(x-np.array([theta]*x.shape[0]))
+            index = 0 if s == 1 else 1
+            Ein[index] = (h_of_x != y).sum()
+        
+        if min(Ein) < best_Ein:
+            best_Ein = min(Ein)
+            if Ein[0] < Ein[1]:
+                sign_ans = 1
+                theta_ans = theta
+            else:
+                sign_ans = -1
+                theta_ans = theta
+
+    return best_Ein/x.shape[0], theta_ans, sign_ans
+            
+
+Ein_log, Eout_log = [], []
+for i in range(2000):
+    x, y = generate_data(8, 0.1)
+    # print(x, y)
+    Ein, theta, sign = decision_stump(x, y)
+    # print(Ein, theta, sign)
+    Ein_log.append(Ein)
+    Eout_log.append(0.5-0.4*sign+0.4*sign*abs(theta))
+
+gap = sorted([ Eout_log[i]-Ein_log[i] for i in range(2000) ])
+median = (gap[999]+gap[1000])/2
+
+plt.scatter(Ein_log, Eout_log)
+plt.xlabel("Ein")
+plt.ylabel("Eout")
+plt.title("median: {}".format(median))
+plt.savefig("hw2_11.png")
+plt.show()
diff --git a/hw2/hw2_12.png b/hw2/hw2_12.png
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index 0000000..8ab1ff7
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diff --git a/hw2/hw2_12.py b/hw2/hw2_12.py
new file mode 100644
index 0000000..75cc8bc
--- /dev/null
+++ b/hw2/hw2_12.py
@@ -0,0 +1,42 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def generate_data(length, noise_prob):
+    x = np.random.uniform(-1, 1, (length, ))
+    x = np.sort(x)
+    y = np.sign(x)
+    noise_mask = ( np.random.rand(length) <= noise_prob  )
+    y[noise_mask] *= -1
+    return x, y
+
+def decision_stump(x, y):
+    theta_seq = np.array([-1] + [(x[i]+x[i+1])/2 for i in range(x.shape[0]-1)])
+    
+    best_Ein = 1e9
+    theta_ans =  np.random.uniform(-1, 1, 1)[0]
+    sign_ans = ( np.random.uniform(-1, 1, 1)[0] > 0 )
+
+    h_of_x = sign_ans * np.sign(x-np.array([theta_ans]*x.shape[0]))
+    Ein = (h_of_x != y).sum()
+    
+    return Ein/x.shape[0], theta_ans, sign_ans
+            
+
+Ein_log, Eout_log = [], []
+for i in range(2000):
+    x, y = generate_data(8, 0.1)
+    # print(x, y)
+    Ein, theta, sign = decision_stump(x, y)
+    # print(Ein, theta, sign)
+    Ein_log.append(Ein)
+    Eout_log.append(0.5-0.4*sign+0.4*sign*abs(theta))
+
+gap = sorted([ Eout_log[i]-Ein_log[i] for i in range(2000) ])
+median = (gap[999]+gap[1000])/2
+
+plt.scatter(Ein_log, Eout_log)
+plt.xlabel("Ein")
+plt.ylabel("Eout")
+plt.title("median: {}".format(median))
+plt.savefig("hw2_12.png")
+plt.show()