Name: ———————-
Practice Quiz - 1
CS 591Q/791V - Pattern Recognition
Posted on: February 19, 2008
Note:
Univariate normal density: N(µ, σ2)=1
√2πσ eh−
1
2(x−µ
σ)2i.
1. [5 points] Briefly describe the following terms: (a) Reject Option; (b) Generative and Discrimina-
tive Models.
2. [8 points] Consider a two-class one-feature classification problem with the following Gaussian
class-conditional densities:
p(x|C1)∼N(0,1),
p(x|C2)∼N1
2,4.
Assume P(C1) = P(C2) = 1/2. Derive the Bayes decision boundary.
3. [7 points] Consider a random variable xhaving the following distribution:
p(x|θ) = θx(1 −θ)1−x.
Suppose that nsamples (x1, x2,...,xn) are drawn independently according to p(x|θ). What is the
maximum likelihood estimate of θ?
1