1. Given probability density function p(x) = 4*x Find the probability (mass function) P(0...

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1. Given probability density function p(x) = 4*x² Find the probability (mass function) P(0<= x <= 1/2) 2. Given the following probability density function for two classes wl and w2 p(x|w1)=0.8e-(x-4)2 and p(x|w2) = 0.8e-(x-5)² and priors P(w1)= 0.4, P(w2) = 0.6 respectively; for the observation is x = 3.0, [2] a) What is the probability that this observation belongs to class wl and w2? [2] b) Given the actions (a1, a2) if x is decided as wl and w2 respectively and the loss function 21(al|w1) = 0.1 and 21(al|w2) = 0.2; what is the expected loss associated with taking action al? [21 1. Given probability density function p(x) = 4*x² Find the probability (mass function) P(0<= x <= 1/2) 2. Given the following probability density function for two classes wl and w2 p(x|w1)=0.8e-(x-4)2 and p(x|w2) = 0.8e-(x-5)² and priors P(w1)= 0.4, P(w2) = 0.6 respectively; for the observation is x = 3.0, [2] a) What is the probability that this observation belongs to class wl and w2? [2] b) Given the actions (a1, a2) if x is decided as wl and w2 respectively and the loss function 21(al|w1) = 0.1 and 21(al|w2) = 0.2; what is the expected loss associated with taking action al? [21

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