# Listing 4
np.random.seed(2)
x1=np.arange(1,10001)
y1=np.zeros(10000)
y1[5000:10000]=1

prob = predict_proba(x1)
fpr, tpr, threshold = roc_curve(y1, prob)

plt.plot(fpr, tpr, 'b')
plt.plot([0,1],[0,1], 'r--')
plt.xlabel("False Positive Rate", fontsize=12)
plt.ylabel("True Positive Rate", fontsize=12)

plt.savefig('random_classifier_roc_inc.png', dpi=300)
plt.show()