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(c) The order of P(t) is 2
Question 4 (4 marks) (a) State TWO advantages of using B-spline curve (b) Given a set of data points Po- (0,0,0), P(...
Derive the basis functions Ni,3(u) and find the equation for the open quadratic B-spline curve defined by five control points p0, p1, p2, p3, and p4.I know the formula is P(u)= the sum of n,i=0(PiNi,k (u))it's difficult to type the formula in this text box. I hope you can understand it.
5. Given knots a-to <ti<..< tn b, and data points (tiy), for i-0,..., n, prove the clamped cubic spline S satisfying S,(a) , S,(b)-β satisfies C2[a,b] interpolating the data points and satisfying g'(a)-α, g'(b)-β. for all g 5. Given knots a-to
5. Given knots a-to <t1 < < tn-b, and data points (ti, yi), for i - 0,... ,n, prove the clamped cubic spline S satisfying S,(a)-a, S,(b) satisfies for all g E C2[a,b] interpolating the data points and satisfying g'(a)-α, g'(b)-β 5. Given knots a-to
Problem 4 - Bayesian inference with uniform prior The data are 21:n, the model is Normal(μ, σ*), with σ2 known. The problem is to obtain the posterior distribution of μ, p(p xỉ n, σ*)p(μ|xì n, σ2) when the prior po(A) is uniform in [-a, a] a. Using Bayes rule, obtain the expression of pĢi X1:n, σ*) as a function of a and the data. Be careful to handle all cases. Give and explicit simple expression for the normaliztion constant. You...
Q1(4 marks) fill in the blank: 1 The process is said to be in control state if two conditions are satisfied: a) b) These are two unnatural patterns of variation within data points in a control chart 2. a) b) 03(20 marks) The bottling machine at JUCE company is being evaluated for its capability BottlingAverage Sample machinestandard deivation Sample size 0.1228 The bottles weight specications are set between 15.8 and 16.2 ounces, and the process mean value is 15.9 ounces...
Question 1 (a) (4 points) What are they key advantages of the Logit model over the Linear Probability Model? (b) (15 points) In class we saw that efficient estimates of the coefficients from a linear regression model can be obtained under the presence of heteroskedasticity using Generalized Least Squares (GLS). How does GLS work? That is, describe the mechanism through which GLS addresses non-constant error variances to achieve efficient estimation. (c) (5 points) Let Zi be the log-odds ratio in...
Question 3 (4 marks) Part a) Given the following information X-500, σ=12, n=50 i) Determine the 95% confidence interval estimate of population mean. ii) Determine the 99% o confidence interval estimate of population mean Part b) A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are X-120 and s-15. (i) Estimate the population mean with 95% confidence level (ii) Estimate the population mean with 99% confidence level.
Question 5 9 marks Consider a Markov chain {YTheN with state space S = {1,2,3,4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 0 0 p 1/6 1/2 1/30 0 4/9 4/9 1/9 0 0 5/6 1/6 2(a) Find the equilibrium probability distribution T (b) Find the probability P(-1%-3. Ya-1). Question 5 9 marks Consider a Markov chain {YTheN with state space S = {1,2,3,4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 0 0 p...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
Given the State Table Below 01 02 Q3 X-1 A. B. C. Draw a state Diagram (S points) Create the "design truth table" for the "next state" and the "output" (5 points) Make a Karnaugh for each "next state" and the "output" (10 points) When making the Karnaugh maps, "xQ1" should be along the top and "O203" along the side (The two missing states should be considered "DONT CARES") Write the "Next State" and Output equations from the Karnaugh maps...
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