Consider a maximization problem that is being solved by Simulated Annealing. Let the objective function value of the current state, s, be 1000. Let this state have 5 successors/neighbors: s1(950), s2(975), s3(1000), s4(1000), and s5(1050). The numbers in parentheses represent the corresponding objective function values. The current temperature is 100. The probability that the next state is: 1. s1 = [Select] 2. s2 = [Select] 3. s3 [Select] = 4. s4= [Select] [Select] 5. s5 0.778 0.121 0.156 0.2 0.606
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- 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.Computer Science Consider the demand and supply system p = ad +bdqd +ud p = as +bsqs +us with the equilibrium condition qd = qs = q. The parameters bd and bs are −2 and 1.5, respectively. Find the parameters ad and as are such that q = 5 and p = 10. Throughout this question use N = 100, and set the random seed to 14022022. The variable ud has a standard deviation of 3. All randomly generated variables have a mean of zero and are normally distributed unless something else is specified. All Monte Carlo studies should be done with 10,000 repetitions. Part a. Illustrate the supply and demand curves in a graph, together with a sample of simulated price and quantity data. Provide an additional graph where you have included the OLS estimated line of demand equation above. Are your estimates close to the true values of ad and bd ? Solve the question in Python language on Jupyter notebook.Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = (-3,-1,0,4} D₂ = {-2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: have and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we p(x | w₁) N, 07) p(x₂)~ N(μ₂, 02). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction?
- 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.Given access to a robot's motion model and prior belief distribution, how can we compute the probability P(x|u) where x is the latest robot's state and u is the control applied at a previous state x'?Please solve the following problem. Quiz = Pass Quiz = Fail AI = Fail 0.1 0.2 AI = Pass 0.6 0.1 Mid = Pass Mid = Fail AI = Fail 0.2 0.2 AI = Pass 0.5 0.1 Suppose you have three events AI Grade, Quiz, and Mid. Here each event has two possible outcomes, either pass or fail. Additionally, given that AI Grade is observed, Quiz and Mid become independent of each other. Also, out of every 100 students, 30 students fail the AI course. Now, using the joint probability tables given, calculate P(AI Grade=Pass, Quiz=Fail, Mid=Fail).
- A nine character long password is to be created using lower-case letters, four special characters {!, @, #, $} and digits. For the password to be valid, it must contain at least one lower-case letter, one of the given special characters and one digit. What is the probability that a randomly generated nine character password is valid? Assume that the password is generated using only the lower-case letters, the given special characters and digitsConsider 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?a. Given n items, where each item has a weight and a value, and a knapsack that can carry at most W You are expected to fill in the knapsack with a subset of items in order to maximize the total value without exceeding the weight limit. For instance, if n = 6 and items = {(A, 10, 40), (B, 50, 30), (C, 40, 80), (D, 20, 60), (E, 40, 10), (F, 10, 60)} where each entry is represented as (itemIdi, weighti, valuei). Use greedy algorithm to solve the fractional knapsack problem. b. Given an array of n numbers, write a java or python program to find the k largest numbers using a comparison-based algorithm. We are not interested in the relative order of the k numbers and assuming that (i) k is a small constant (e.g., k = 5) independent of n, and (ii) k is a constant fraction of n (e.g., k = n/4). Provide the Big-Oh characterization of your algorithm.
- Consider the challenge of determining whether a witness questioned by a law enforcement agency is telling the truth. An innovative questioning system pegs two individuals against each other. A reliable witness can determine whether the other individual is telling the truth. However, an unreliable witness's testimony is questionable. Given all the possible outcomes from the given scenarios, we obtain the table below. This pairwise approach could then be applied to a larger pool of witnesses. Answer the following: 1) If at least half of the K witnesses are reliable, the number of pairwise tests needed is Θ(n). Show the recurrence relation that models the problem. Provide a solution using your favorite programming language, that solves the recurrence, using initial values entered by the user.Suppose we use the following KB (where x,y,z are variables and r1, r2, r3, goal are constants) to determine whether a particular robot can score a) Open(x) ∧ HasBall(x) -> CanScore(x) b) Open(x) ∧ CanAssist(y,x) ∧ HasBall(y) -> CanScore(x) c) PathClear(x,y) -> CanAssist(x,y) d) PathClear(x,z) ∧ CanAssist(z,y) -> CanAssist(x,y) e) PathClear(x,goal) -> Open(x) f) PathClear(y,x) -> PathClear(x,y) g) HasBall(r3) h) PathClear(r1, goal) i) PathClear(r2, r1) j) PathClear(r3, r2) k) PathClear(r3, goal) Intuitively, CanScore(x) means x can score on goal. CanAssist(x,y) means there exists some series of passes that can get the ball from x to y. Open(x) means x can shoot on goal directly. And PathClear(x,y) means the path between x and y is clear. Provide a SLD-derivation for the query CanScore(x) in which the answer provided is r1. Provide a SLD-derivation for the query CanScore(x) in which the answer provided is r3. How many "distinct" derivations (i.e., involving different…A seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Suppose the buyer uses a strategy p1(b) = 1/12 + (2/3)b and the seller uses a strategy p2(s) = 1/4 + (2/3)s. Suppose the buyer's value is 3/4 and the seller's valuation is 1/4. Will there be a transaction? Explain. Is this strategy profile a Bayesian Nash equilibrium? Explain.