Consider two nonnegative numbers a and b, and show that, if a lessthanorequalto b, then a lessthanorequalto (ab)^1/2. Use this result to show that, if the decision regions of a two-class classification problem are chosen to minimize the probability of misclassification, this probability will satisfy. p (mistake) lessthanorequalto integral (p (x, C_1) p (x, C_2))^1/2 dx p (mistake) lessthanorequalto integral_R1 p (x, C_2) dx + integral_R2 p (x, C_1) dx and apply Bayes rule. Consider two nonnegative numbers a and b, and show that, if a lessthanorequalto b, then a lessthanorequalto (ab)^1/2. Use this result to show that, if the decision regions of a two-class classification problem are chosen to minimize the probability of misclassification, this probability will satisfy. p (mistake) lessthanorequalto integral (p (x, C_1) p (x, C_2))^1/2 dx p (mistake) lessthanorequalto integral_R1 p (x, C_2) dx + integral_R2 p (x, C_1) dx and apply Bayes rule