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(c) The order of P(t) is 2
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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(...
5. Given knots a-to <ti<..< tn b, and data points (tiy), for i-0,..., n, prove the clamped cubic spline S sati...
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...
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
matlab 2) Plots the individual points with "star" marks b) Fisa cubie spline to the data...
matlab
2) Plots the individual points with "star" marks b) Fisa cubie spline to the data use "o" marks c) Fits a 5th order polynomial use "x" marks 3) MATLAB contains functions to calculate the natural logarithm (log), the logarithm to the base 10 (log 10), and the logarithm to the buse 2 (log2). However, if you want to find a logarithm to another base for example, base - you'll have to do the math yourself with the formula log)(x)...
The Bezier curve in the following figure is defined by 4 control points. P,-(0. O), Pi...
The Bezier curve in the following figure is defined by 4 control points. P,-(0. O), Pi = (1, 1), P2 (3, 2), Ps- (4, 0). a) b) Find the equation of the Bezier curve Find the point on the curve at u 0.5 1 0
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) wh...
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 ch...
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 3 (4 marks) Part a) Given the following information X-500, σ=12, n=50 i) Determine the...
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 7. (15 marks] Consider the discrete time system given by the state equation 07 x4...
Question 7. (15 marks] Consider the discrete time system given by the state equation 07 x4 + 11-18 8/11 - 10/n VIK) = 10 11 **) 1. [3 marks) Determine if the system is (a) Lyapunov state, syptereally ) Bounded input Bounded Output (BIBO) stable. Provide brief explanations 2. (8 marks) Design a discrete-time state feedback control law of the form - Kxkl by finding the gain K to place the closed-loop eigenvalues at 0.5 3. [4 marks) Suppose the...
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...
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...
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/...
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...
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
matlab
2) Plots the individual points with "star" marks b) Fisa cubie spline to the data use "o" marks c) Fits a 5th order polynomial use "x" marks 3) MATLAB contains functions to calculate the natural logarithm (log), the logarithm to the base 10 (log 10), and the logarithm to the buse 2 (log2). However, if you want to find a logarithm to another base for example, base - you'll have to do the math yourself with the formula log)(x)...
The Bezier curve in the following figure is defined by 4 control points. P,-(0. O), Pi = (1, 1), P2 (3, 2), Ps- (4, 0). a) b) Find the equation of the Bezier curve Find the point on the curve at u 0.5 1 0
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 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 7. (15 marks] Consider the discrete time system given by the state equation 07 x4 + 11-18 8/11 - 10/n VIK) = 10 11 **) 1. [3 marks) Determine if the system is (a) Lyapunov state, syptereally ) Bounded input Bounded Output (BIBO) stable. Provide brief explanations 2. (8 marks) Design a discrete-time state feedback control law of the form - Kxkl by finding the gain K to place the closed-loop eigenvalues at 0.5 3. [4 marks) Suppose the...
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...
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...
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