How do I find P(A) and also P(B) given P(C) P(C') P(AlC) P(BlC) P(AlC') and P(BlC'). And how do I find out if P(A) and P(B) are independent?
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Conditional Probability
How do I find P(A) and also P(B) given P(C) P(C') P(AlC) P(BlC) P(AlC') and P(BlC').
And how do I find out if P(A) and P(B) are independent?
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- (control variates) Reproduce the class example of estimating int 0 ^ 1 2 dz 1+x by the MC approach using 100 uniform random variables and after that by using a control variate with function g(U) = 1 + U as suggested in class. Compare the results.We consider a Bayesian network with 74 variables including Variables A, B, and C. If we want to study inference P(A|B,C), how many hidden variables are there?Computer Science Suppose that the family is a (d1, d2, p1, p2)-sensitive LSH family. What does this mean specifically with respect to the distance parameters d1 < d2 and the probability parameters p1 > p2? What is the false positive rate and the false positive rate of the family?
- Match the following sentence to the best suitable answer: - A. B. C. D. "in how many ways a four-letter word can beformed from the letters A, B, C, D and E, where the word cannot start or end with the letter C. repetition is allowed" - A. B. C. D. The event of non-occurrence of another event in an probabilistic experiment E is called the - A. B. C. D. An/A _____________ is any subset of outcomes contained in the sample space. - A. B. C. D. nPn = A. Complementary Event B. event E C. 4 x 5 x 5Êx 4 = 400 D. n!2. Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and Event B = {3, 7, 9, 11, 12, 13} Find the probability P(A|B). State your answer as a value with one digit after the decimal point.When a temperature gauge surpasses a threshold, your local nuclear power station sounds an alarm. Core temperature is gauged. Consider the Boolean variables A (alarm sounds), FA (faulty alarm), and FG (faulty gauge) and the multivalued nodes G (gauge reading) and T (real core temperature). Since the gauge is more likely to fail at high core temperatures, draw a Bayesian network for this domain.
- A Bayesian network has four variables: C,S,R,W, where -- C is independent, with P(C)=0.5 -- S is conditional on C, with P(S|C)=0.1, and P(S|~C)=0.5 -- R is conditional on C, with P(R|C)=0.8, and P(R|~C)=0.2 -- W is conditional on S and R, with P(W|S,R)=0.99, P(W|S,~R)=0.9, P(W|~S,R)=0.9,P(W|~S,~R)=0. a) List possible states of this world.b) Calculate the probability P(R|S).Use rules of inference to show that if ∀x(P (x) ∨ Q(x)) and ∀x((¬P (x) ∧ Q(x)) → R(x)) are true, then ∀x(¬R(x) → P (x)) is also true, where the domains of all quantifiers are the sameConsider a logistic regression classifier that implements the 2-input OR gate. At iteration t, the parameters are given by w0=0, w1=0, w2=0. Given binary input (x1,x2), output of logistic regression is given by 1/(1+exp(-w0-w1*x1-w2*x2)). What will be value of the loss function at t? What will be the values of w0, w1 and w2 at (t+1) with learning rate ɳ=1?
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