A Bayesian Network that represents the relationship between accidents and weather conditions is shown below. Cloudy? P(Cloudy) Cloudy True 0.75 Fill the joint distribution table from the above Bayesian Network. Cloudy Freezing Accident P(Cloudy, Freezing, Accident) True True True 0.2 False 0.05 True True True False True True False False False True True False True False False False True False False False Freezing? P(Freezing) True 0.333 Freezing Cloudy? Freezing? P(Accident=true❘ Cloudy, Freezing) Accident True True 0.8 True False 0.5 False True 0.6 False False 0.1 Calculate the answers to these queries (hint: the joint distribution can be used to answer any query): What is the probability that an accident will occur? What is the probability that it is Cloudy and an Accident occurs? What is the probability that it is Cloudy if it is known that an Accident occurred? What is the probability that an accident will not occur if it is known that it is Cloudy and it is Freezing? P(Cloudy=True, Freezing=False, Accident=True) [Choose ] P(Cloudy=True, Freezing=False, Accident=False) P(Cloudy=False, Freezing=True, Accident=True) P(Cloudy=False, Freezing=True, Accident=False) P(Cloudy=False, Freezing=False, Accident=True) 0.45 0.871 0.2 [Choose ] P(Cloudy=False, Freezing=False, Accident=False) [Choose ] Probability that an accident will occur? Probability that it is Cloudy and an Accident occurs? [Choose ] [Choose ] Probability that it is Cloudy if it is known that an Accident occurred? [Choose ] Probability that an accident will not occur if it is known that it is Cloudy [Choose ] and it is Freezing?

2. Can you design a binary classification experiment with 100 total population (TP+TN+FP+ FN), with precision (TP/(TP+FP)) of 1/2, with sensitivity (TP/(TP+FN)) of 2/3, and specificity (TN/(FP+TN)) of 3/5? (Please consider the population to consist of 100 individuals.)

The gasoline price often varies a great deal across different regions across country X. The followingdata show the price per gallon for regular gasoline for a random sample of gasoline service station forthree major brands of gasoline (A, B and C) located in 10 metropolitan areas across the country X.A B C3.77 3.83 3.783.72 3.83 3.873.87 3.85 3.893.76 3.77 3.793.83 3.84 3.873.85 3.84 3.873.93 4.04 3.993.79 3.78 3.793.78 3.84 3.793.81 3.84 3.86 State the null and alternative hypothesis for single factor ANOVA to test for any significant difference in the mean price of gasoline for the three brands