How many Matlab seat licenses are required for there to be a~1% steady state probability
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- 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?A version of simple exponential smoothing can beused to predict the outcome of sporting events. To illustrate,consider pro football. We first assume that all games areplayed on a neutral field. Before each day of play, we assumethat each team has a rating. For example, if the Bears’ ratingis 10 and the Bengals’ rating is 6, we would predict theBears to beat the Bengals by 10 6 4 points. Supposethe Bears play the Bengals and win by 20 points. For thisobservation, we “underpredicted” the Bears’ performanceby 20 4 16 points. The best a for pro football is 0.10.After the game, we therefore increase the Bears’ rating by16(0.1) 1.6 and decrease the Bengals’ rating by 1.6 points.In a rematch, the Bears would be favored by (10 1.6) (6 1.6) 7.2 points. a How does this approach relate to the equation At=At1 a(et)?b Suppose the home-field advantage in pro football is 3 points; that is, home teams tend to outscore visiting teams by an average of 3 points a game. How could the home-field advantage…This is to be done in MATLAB. Thanks! MISSION: Build a script (use the Live Script in MATLAB) that produces the derivative of the function f(x)=exp(−x)cos(x) between x=−5 and x=5 by applying both, the Forward Difference and Centered Difference approximations. Compare the numerically-determined derivatives with the actual derivative (product rule) by plotting all three curves on the same graph. Demonstrate graphically that the accuracy of the numerical derivative increases as the interval Δx decreases. It would be most effective to plot all three curves on the same graph for a given value of Δx. End up with a separate graph, demonstrating the comparison of all three curves, for each value of Δx chosen. Also, describe the "numerical approach," i.e. the method used to approximate the derivative. Thus, a clear description of the numerical approach at the beginning of the Live Script, and a detailed demonstration of how accuracy increases by systematically lowering Δx is expected as part of…
- A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 . f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0 (a) Using M_{X}(t) or otherwise, find the mean and variance of X. (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.Generate 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 ProgrammingUse R to answer the following question According to the central limit theorem, the sum of n independent identically distributed random variables will start to resemble a normal distribution as n grows large. The mean of the resulting distribution will be n times the mean of the summands, and the variance n times the variance of the summands. Demonstrate this property using Monte Carlo simulation. Over 10,000 trials, take the sum of 100 uniform random variables (with min=0 and max=1). Note: the variance of the uniform distribution with min 0 and max 1 is 1/12. Include: 1. A histogram of the results of the MC simulation 2. A density plot of a normal distribution with the appropriate mean and standard deviation 3. The mean and standard deviation of the MC simulation. ps(plz do not use chatgpt)
- We are intrested in predicting the percentage of people commuting to work by walking given some input variables. Each observation corresponds to a different city and each input variable summarizes some characteristic of a given city, such as density, urban sprawl and average income per capita. This is 1. not a machine learning problem. Only social scientists would be interested in such a problem. 2. both a classification and a regression problem as it depends on the way one codes the output variable as either 0, 1 or a a particular number in the [0,1] interval. 3. a regression problem. The output variable is continuous. 4. a classification problem. Walking to work is a discrete variable and can only take two values: to walk to work and not to walk to worUsing the MATLAB Histogram function, "hist.m", Illustrate the Central Limit Theorem by taking two different random variables and show how when appropriately scaled and summed, they converge to a Normal (Gaussian) distribution.Assume that the entire sample has 8 positive observations and 4 negatives observations. Variable X1: at the left branch has 9 positive observations and 3 negatives observations;at the right branch has 8 positive observations and 8 negatives observations. What is the information gain or reduction in uncertainty of X1 using the Gini index? (round to two decimal spaces)
- Do it on R (using Pnorm) A process yields 10% defective items. If 100 items are randomly selected from the process, what is the probability that the number of defectives (a) exceeds 13? (b) is less than 8?The task is to implement density estimation using the K-NN method. Obtain an iidsample of N ≥ 1 points from a univariate normal (Gaussian) distribution (let us callthe random variable X) centered at 1 and with variance 2. Now, empirically obtain anestimate of the density from the sample points using the K-NN method, for any valueof K, where 1 ≤ K ≤ N. Produce one plot for each of the following cases (each plotshould show the following three items: the N data points (instances or realizations ofX) and the true and estimated densities versus x for a large number – e.g., 1000, 10000– of discrete, linearly-spaced x values): (i) K = N = 1, (ii) K = 2, N = 10, (iii) K = 10,N = 10, (iv) K = 10, N= 1000, (v) K = 100, N= 1000, (vi) K = N = 50,000. Pleaseprovide appropriate axis labels and legends. Thus there should be a total of six figures(plots),ANY help would be greatly appreciated. From 1965 to 1974, in U.S. there were M= 17,857,857 male livebirths and F= 16,974,194 female livebirths. We model the number of male livebirth as a binomial distribution withparameterssize = M+F and prob = p. The following code computes the maximum likelihood estimator for p. male = 17857857 female = 16974194 ll <-function(p){dbinom(male, size = male+female, prob=p, log=TRUE) } ps <-seq(0.01, 0.99, by = 0.001) ll.ps <-ll(ps) plot(ps, ll.ps, type='l') phat <- ps[which.max(ll.ps)] abline(v = phat, col='blue') QUESTION: For this problem, can you give a theoretical formula for the maximum likelihood estimator,ˆp, usingMandF? (No need to compute the numerical value.)