Exercise 4.23 - Scalar QDA

import math 
hm=[67,79,71] 
hf=[68,67,60] 
def mu(h): 
   return (h[0]+h[1]+h[2])/3 
def sigma2(h): 
   m=mu(h) 
   return ((h[0]-m)**2+(h[1]-m)**2+(h[2]-m)**2)/3 
# For question (a): 
mu_m=mu(hm) 
mu_f=mu(hf) 
sigma2_m=sigma2(hm) 
sigma2_f=sigma2(hf) 
print(mu_m) 
print(sigma2_m) 
print(mu_f) 
print(sigma2_f) 
# \pi_{m}=\pi_{f}=0.5. 
# For question (b): 
temp_m=(2*math.pi*sigma2_m)**(-0.5)*math.exp(-(72-mu_m)**2/2/sigma2_m) 
temp_f=(2*math.pi*sigma2_f)**(-0.5)*math.exp(-(72-mu_f)**2/2/sigma2_f) 
print(temp_m/(temp_m+temp_f))

For question (c) we can use a naive Bayes model, which is tantamount to adopting diagonal covariance matrices for both classes.