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We have considered, in the context of a randomized
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- 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.Consider 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?Suppose you have two boxes A and B. Box A contains 7 black marbles, 4 white marbles. Box B contains 7 white and 4 black marbles. A random experiment is performed in two sequential trials by first drawing a marble randomly from box A and putting into Box B. In the second trial after the first trial, a marble is drawn randomly from box B. If we reverse the scenario, then what is the probability of drawing a black marble from box A given that a white marble is drawn from box B.
- (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.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.Write Algorithm for Generating a random number from a distribution described by a finite sequence of weights.in: sequence of n weights W describing the distribution (Wi ∈ N for i = 0, . . . , (n − 1) ∧ 1 ≤ n−1 i=0 Wi)out: randomly selected index r according to W (0 ≤ r ≤ m − 1)
- 3. Give an example of a random variable X that takes on values from the set of all binary strings of length 4 where the min-entropy of X and the entropy of X are very different. Explain what is causing this phenomenon.A certain cat shelter has devised a novel way of making prospective adopters choose their new pet. To remove pet owners’ biases regarding breed, age, or looks, they are led blindfolded into a room containing all the cats up for adoption and must bring home whichever they pick up. Suppose you are trying to adopt two cats, and the shelter contains a total of N cats in one of only two colors: black or orange. is it still possible to pick up two black cats with probability ½, given that there is an even number of orange cats in the room? If so, how many cats should be in the room? How many black, how many orange?Imagine that you have a problem P that you know is N P-complete. For this problem you have two algorithms to solve it. For each algorithm, some problem instances of P run in polynomial time and others run in exponential time (there are lots of heuristic-based algorithms for real N P-complete problems with this behavior). You can’t tell beforehand for any given problem instance whether it will run in polynomial or exponential time on either algorithm. However, you do know that for every problem instance, at least one of the two algorithms will solve it in polynomial time. (a) What should you do? (b) What is the running time of your solution? 564 Chap. 17 Limits to Computation (c) What does it say about the question of P = N P if the conditions described in this problem existed?
- . The vacuum cleaner problem is a well-known search problem for a vacuum cleaner robot that works on Artificial Intelligence. In this problem to clean up the whole area. In the superficial world, the vacuum cleaner agent has a location sensor and a dirt sensor to know where it is (room A, room B, or any n room) and whether the room is dirty. Also, the robot needs to avoid the obstacle (stool) and find a new path. A possible performance measure is to maximize the number of clean rooms over a certain period. For this problem, four main conditions should be considered: in(x,y) means a robot at (x,y) dirt(x,y) means there is a dirt at(x,y) facing(d) means the robot is facing direction d, where d ={north, east, south, west} • hit(s) means the robot hits the obstacle s possible actions the robot can do - turn, forward, suck-dirt, avoid a) Write possible rules that can be used to perform the room cleaning plan b) Execute this plan…Write a python program by following rules: Has ? discrete time intervals where ? is large. Generates a set of customer call arrivals with the arrival rate of ? at random locations in the ? intervals (e.g., for each interval, a call will happen with probability ?/?). Counts the number of calls that actually occurs during these ? intervals. Design your experiment to determine the Poisson distribution of this experiment (probability of having k arrivals in n intervals).Write Algorithm to Generating a random number from a distribution described by a finite sequence of weights.in: sequence of n weights W describing the distribution (Wi ∈ N for i = 0, . . . , (n −1) ∧ 1 ≤ n−1 i=0 Wi)out: randomly selected index r according to W (0 ≤ r ≤ m − 1)