A probability distribution on the real line is a mixture of two classes +1 and−1 with density N(1,2) (normal distribution with m
A probability distribution on the real line is a mixture of two classes +1 and−1 with density N(1,2) (normal distribution with mean1 and variance 2) andN(3,1), with prior probabilities (probability of eachclass) 0.4 and 0.6 respectively. What is the Bayes decision rule? Give anestimate for the Bayes risk.
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Answer:
See explanation
Step-by-step explanation:
Let x be the number of simple arrangements and y be the number of grand arrangements.
1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so
2. A florist can make a grand arrangement in 18 minutes hour, then he can make y arrangements in
hours.
A florist can make a simple arrangement in 10 minutes hour, so he can make x arrangements in
hours.
The florist can work only 40 hours per week, then
3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.
The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.
Total profit: $(10x+25y)
Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines and
But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is
