b) What is the mathematical expression for how many candies you need to unwrap before you are more
90% sure which type of bag you have? (5 P.)
c) Make a plot that illustrates the revuction in variabilty of the curves for the posterior probability for each
type of bag by averaging each curve obtained from multiple datasets. (15 P.)
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Q3. Classification with Gaussian Mixture Models
Suppose you have a random variable which is drawn from one of two classes C1 and C2. Each class follows
a Gaussian distribution with means u1 and u2 (assume u1 < 42) and variances 01 and o2. Assume that the
prior probability of C1 is twice that of C2.
a) What is the expression for the probability of x, i.e. p(2), when the class is unknown? (5P.)
b) What is the expression for the probability of total error in this model assuming that the decision bound-
ary is at x = 0? (10 P.)
c) Derive an expression for the value of the decision boundary O that minimizes the probability of misclas-
sification. (10 P.)
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