nown that a natural. law obeys the quadratic relationship y=ax^2. what is the best line of form y=px+q that can be used to model data and minimise Mean-squared-error, if all of the data points are drawn uniformly
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it is known that a natural. law obeys the quadratic relationship y=ax^2.
what is the best line of form y=px+q that can be used to model data and minimise Mean-squared-error, if all of the data points are drawn uniformly at random from the domain [0,1]?
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- Solve in R programming language: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3. (a) Find p(X<1.25). (b) Find EX. (c) Find the variance of X.<s> I am Sam </s><s> Sam I am </s><s> I am Sam </s> <s> I do not like green eggs and Sam </s> If we use linear interpolation smoothing between a maximum-likelihood bigram model and a maximum-likelihood unigram model with lambda1 = 1⁄2 and lambda2=1⁄2, what is P(Sam|am)? Include <s> and </s> in your counts just like any other token.Consider another case in which a = 6,286, Xo = 4,985, C = 3,079 and M = 487.i). using the linear congruential method, determine the first 10 random numbers.ii). How robust is this algorithm?
- 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?The room temperature x in Fahrenheit (F) is converted to y in Celsius (C) through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?The room temperature x in Fahrenheit is converted to y in Celsius through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?
- 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.)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)1. Describe how linear regression can be used on the exponential function in a meaningful way noting that it is not a linear function. 2. Describe two different aspects between closed (bracketed) and open root-finding methods.
- (Do it on R)(using Pnorm) The loaves of rye bread distributed to local stores by a certain bakery have an average length of 30 centimeters and a standard deviation of 2 centimeters. Assuming that the lengths are normally distributed, what percentage of the loaves are (a) longer than 31.7 centimeters? (b) between 29.3 and 33.5 centimeters in length? (c) shorter than 25.5 centimeters?Linear regression aims to learn the parameters 7 from the training set D = {(f(),y(i)), i {(x(i),y(i)),i = 1,2,...,m} so that the hypothesis ho(x) = ēr i can predict the output y given an input vector š. Please derive the least mean squares and stochastic gradient descent update rule, that is to use gradient descent algorithm to update Ô so as to minimize the least squares cost function JO).Computer Science Suppose we have 3 independent classifiers, each of which can correctly predict the label of a data point with 80% accuracry. Using the hard voting approach, prove that the ensemble of these classifiers can correctly predict with at least 89% accuracy.