Can you please explain me question 1, 3, 4 and 5 of the document attached below

1. QUESTION 1 Consider the joint probability distributions of three Boolean variables as shown below: What are the prior probabilities of smart and study i.e. P(smart) and P(study) P(Smart) = 0.3 P(Study) = 0.4 P(Smart) = 0.6 P(Study) = 0.4 P(Smart) = 0.6 P(Study) = 0.8 P(Smart) = 0.8 P(Study) = 0.6 10 points 1. QUESTION 2 Using the data presented in question 1, evaluate the following conditional probability: P(Prepared | Smart ^ Study) 0.8 1 0.9 0.7 2 0.6 10 points 1. QUESTION 3 Using the data from question 1, evaluate the following: P(Smart|Study) 0.8 0.6 0.9 1 0.8 2 10 points QUESTION 4 1. Using the data from question 1, what can you infer about the relationship between smart and study Smart and study are independent Smart and study are dependent Nothing can be said for sure about the relationship between smart and study None of the above are true 10 points 1. QUESTION 5 Consider the simple Bayes Net shown below: You are given the following values (known as parameters in a Bayes Net): The probability of smoking in the entire population is 1.0%. Given that someone smokes, their probability of cancer is 40%. Which of the following queries can you evaluate using these values: P(Cancer| Smoking) P(Smoking) P(Smoking| Cancer) P(Cancer) 10 points 1. QUESTION 6 Using the data and the parameters of question 5, suppose you are given the additional information that the probability a non-smoker has cancer is 10%. Which of the following probabilities can you now evaluate? P(Cancer) P(Smoking|Cancer) P( Smoking| Cancer) P( Cancer) 10 points 1. QUESTION 7 Which of the following is the correct statement for the Markov condition for the Bayes net Given its parents, a node is conditionally independent of its nondescendants. Given its parents, a node is conditionally independent of its children nodes. Given its parents, a node is conditionally dependent on its non-descendants Given its parents, a node is conditionally independent of its grandchildren nodes 10 points QUESTION 8 1. Given the Bayes Net below: Compute the following joint probability: P( B, E, A, J, M) 0.00051 2 0.00025 6 0.00102 4 0.00076 8 10 points Click Save and Submit to save and submit. Click Save All Answers to save all answers