Homework 1, Statistical Pattern Recognition, Summer 2014, Bochum

Question 1

a) In ECE at Purdue in 2013, there were 4 times as many female students with hair shorter than 30cm as with hair longer than 30cm. There were, on the other hand, 9 times as many male students with hair shorter than 30cm as with hair longer than 30cm. Assuming that the male population was 85% of the Purdue ECE population at that time, what is the more likely gender of a Purdue ECE student with hair length longer than 30cm? (Explain your reasoning briefly.)

b) In ECE at Purdue in 2013, there were 30 female students with hair longer than 30cm, and 85 male students with hair longer than 30cm. what is the more likely gender of a Purdue ECE student with hair length longer than 30cm? (Explain your reasoning briefly.)

c)Which problem among a) or b) above corresponds to Bayes decision rule? Why is that approach to making more decision more practical than the other approach? (Explain briefly.)

Question 2

For this problem, we view hair length as a continuous-valued feature vector x>0. Assume that the pdf p(x|female) is a chi-squared distribution with mean 6. Assume that the pdf p(x|female) is a chi-squared distribution with mean 4. a) Obtain the regions R1 and R2 for this decision problem? b) GIve two possible discriminant functions for this decision problem.