y train a linear function ing stochastic gradient = 0.1,0₁ = 0.1, 02 = C
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- please try to simulate the probability of rolling a Die with Sample Space* S={1,2,3,4,5,6} and the probability of each sample point has a 1/6 chance of occurring, i.e., you need to verify that your simulation converges to 1/6 when you select one point of sample space. When X is a random variable for sample point of rolling a Die, Pr(X<=4)=2/3. Please verify this result by simulation. Please let me know how to make an Excel file as stated above.Manually train a hypothesis function h(x) = g(ỗ¹x) based on the following training instances using stochastic gradient ascent rule. The initial values of parameters are 0o = 0.1,0₁ = 0.1, 0₂ = 0.1. The learning rate a is 0.1. Please update each parameter at least five times. X1 0 0 1 1 X2 0 1 0 1 y 1 1 0 0SIMULATION AND MODELING Using the mid- square method obtain the random variables using Z0= 1009 until the cycle degenerates to zero.
- We can specify the PageRank algorithm's convergence threshold using proc networks. This figure has to be positive. Default value is 1E-9. When the difference between the PageRank scores of the current iteration and the previous iteration is less than or equal to the tolerance set, the PageRank algorithm ceases iterating. We can use the PAGERANKTOLERANCE= parameter to specify the convergence tolerance. Write The example code demonstrates how to calculate PageRank centrality using a proc network built on a directed graph with unweighted links.Write a program to find the solution to Maxone problem (You want to maximize the number of ones) using agenetic algorithm where the population size is 2000 and each chromosome is 20 genes long. Use a mutationprobability of 0.02 and a cross-over probability of 0.5. Make separate functions for different components of thegenetic algorithm.Considering the problem of performing rapid COVID test among a large group of people. Assuming there are exactly 1 positive case among N people, and you are asked to find the positive case with the least number tests. 1. A straight forward approach is to test every single person, which requires N tests in total. Can you design a testing framework that works better than the greedy one under, even under the worst-case scenario? Write the pseudo code for your approach and briefly explain the time complexity of your approach. 2. Based on your framework, if there are 1,000 people, what are the maximum number of tests that need to be performed in order to identify the positive case (number of tests required in the worst case)?
- Recall the Monte Carlo method, from week 6 (section 6.2.2), for approximating . Suppose we choose a point (x, y) randomly (with uniform distribution) in the unit square. The probability that it lies inside a circle of diameter 1 contained in the unit square is equal to the area of that circle, or π/4. So this Monte Carlo method works as follows: Write a function montecarlo (M) which takes an integer M and returns an approximation to π. (I can't give you an example output, as the random nature of the procedure means approximations will differ!)Determine the decision parameter p for the Bresenham's circle drawing procedure. The stages of Bresenham's circle drawing algorithm are listed.Remaining Time: 2 hours, 27 minutes, 02 seconds. Duestion Completion Status: Y=A'. B' + (AOB) b. Using Karnaugh map, simplify the following Boolean function F (show your grouping): [2 Marks] A B C F 1 1 1 1 1 1 1 1 1 0. 1 1 1 1 1 1 Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All A O Type here to search DLL FS F9 F10 F11 9 3 r 7 Y 8 W E R = G i JJ 立
- Find the global minimum of the function y = F (x)(function 1 variable)using a climbing algorithm Climbing algorithm1. start at a random point x0 def. field on the x-axis, evaluate the function y = F (x0)2. search the neighbors left and right at a distance of 1 step d, evaluate the function in points y = F (x0-d), y = F (x0 + d)3. if the value of the function is lower at any of these points, it moves the current solution to this new position4. if the required number of steps has been performed or a smaller value of y is no longer found, end, otherwise continue in point 2Generate 100 synthetic data points (x,y) as follows: x is uniform over [0,1]10 and y = P10 i=1 i ∗ xi + 0.1 ∗ N(0,1) where N(0,1) is the standard normal distribution. Implement full gradient descent and stochastic gradient descent, and test them on linear regression over the synthetic data points. Subject: Python ProgrammingFor all positive numbers aaand bbwith a>ba>b, ln(a−b)=ln(a)/ln(b)ln(a−b)=ln(a)/ln(b) True or false