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Question 4 Consider a p-variate sample with size T1.,n For some CE RxP and a E R9, consider the l...
Question 6 Consider two independent samples from 3-variate multivariate normal populations: 3 2 2 S2 3 2 1411 Population 1 with 12: sample size n 10, 13 3 2 21 Population 2 with 2 22sample size...
Question 6 Consider two independent samples from 3-variate multivariate normal populations: 3 2 2 S2 3 2 1411 Population 1 with 12: sample size n 10, 13 3 2 21 Population 2 with 2 22sample size n2 - 10, 6,S2 2 3 2 μ21 23 Furthermore, assume the population covariance matrices of the two populations are the same. We aim to test 1. Test Ho with a 0.05 by Hotelling's T2 2. Test Ho with α 0.05 by Bonferroni correction....
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x...
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x = n-ı Σ i , and y = n-ı Σ -1 y be the sample means of the x and y variables. Let & and Sy be the corresponding standard deviations. Let sry and rry be the sample covariance and sample correlation respective . Suppose x = 6.2,J = 8 8 2.95, sy4.494, sy 13.05. Part a) What is the sample correlation of the...
Consider the following bivariate data. Point A B C D E F G H I J...
Consider the following bivariate data. Point A B C D E F G H I J x 0 6 5 6 0 0 2 5 1 0 y 5 3 1 5 3 6 4 6 5 0 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Calculate the covariance. (Give your answer correct to two decimal places.) (c) Calculate sx and sy. (Give...
Consider the following bivariate data. Point A B C D E F G H I J...
Consider the following bivariate data. Point A B C D E F G H I J x 4 3 0 4 7 1 6 5 7 2 y 4 6 7 0 7 7 3 3 7 1 (b) Calculate the covariance. (Give your answer correct to two decimal places.) A = -0.167 (c) Calculate sx and sy. (Give your answers correct to three decimal places.) sx = sy = (d) Calculate r using formula 13.2. (Give your answer correct...
Consider the following bivariate data. Point A B C D E F G H I J...
Consider the following bivariate data. Point A B C D E F G H I J x 1 4 6 6 4 3 7 4 5 0 y 7 6 3 4 0 6 2 0 6 3 (a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Calculate the covariance. (Give your answer correct to two decimal places.) (c) Calculate sx and sy. (Give...
R programming: it is the whole question. no more data Problem Five: Below are some statistical...
R programming: it is the whole question. no more data
Problem Five: Below are some statistical summaries of the two variables “Age" as the predictor and "MaxHR" as the response. The sample size for this data is 303. summary (Age) Min. ist Qu Median 29.00 48.00 56.00 54.44 61.00 77.00 var(Age) Mean Max [1] 81.69742 0 23182.6 20.a >summary (MaxHR) Min. lst Qu. Median Mean 3rd Qu 71.0 133.5 153.0 149.6 166.0 202.0 var(MaxHR) [1] 523.2658 [1] 2443182 sum (MaxHR...
1. Write R' = {(x, y) |X, Y ER} to represent the set of all 1x2...
1. Write R' = {(x, y) |X, Y ER} to represent the set of all 1x2 row vectors of real numbers. This is the standard Euclidean plane you all know and love. If such a row vector is multiplied on the right by a 2x2 matrix, then the output is again in R"; such matrices are called linear transformations. 1. Find a linear transformation that rotates the plane R by a radians. That is, find a matrix T such that...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
2. Let F be a field, n > 1 an integer and consider the F-vector space Mat,,n(F) of n × n matrices over F. Given a m...
2. Let F be a field, n > 1 an integer and consider the F-vector space Mat,,n(F) of n × n matrices over F. Given a matrix A = (aij) E Matn,n(F) and i < n let 1 row,(Α-Σ@y and col,(A)-Žaji CO j-1 j-1 be the sum of entries in row i and column i, respectively. Define C, A EMat,,(F): row,(A)col,(A) for all 1 < i,j < n] C, { A E Matn.n(F) : row,(A) = 0 = col,(A) for...
Question 6 Consider two independent samples from 3-variate multivariate normal populations: 3 2 2 S2 3 2 1411 Population 1 with 12: sample size n 10, 13 3 2 21 Population 2 with 2 22sample size n2 - 10, 6,S2 2 3 2 μ21 23 Furthermore, assume the population covariance matrices of the two populations are the same. We aim to test 1. Test Ho with a 0.05 by Hotelling's T2 2. Test Ho with α 0.05 by Bonferroni correction....
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x = n-ı Σ i , and y = n-ı Σ -1 y be the sample means of the x and y variables. Let & and Sy be the corresponding standard deviations. Let sry and rry be the sample covariance and sample correlation respective . Suppose x = 6.2,J = 8 8 2.95, sy4.494, sy 13.05. Part a) What is the sample correlation of the...
R programming: it is the whole question. no more data
Problem Five: Below are some statistical summaries of the two variables “Age" as the predictor and "MaxHR" as the response. The sample size for this data is 303. summary (Age) Min. ist Qu Median 29.00 48.00 56.00 54.44 61.00 77.00 var(Age) Mean Max [1] 81.69742 0 23182.6 20.a >summary (MaxHR) Min. lst Qu. Median Mean 3rd Qu 71.0 133.5 153.0 149.6 166.0 202.0 var(MaxHR) [1] 523.2658 [1] 2443182 sum (MaxHR...
1. Write R' = {(x, y) |X, Y ER} to represent the set of all 1x2 row vectors of real numbers. This is the standard Euclidean plane you all know and love. If such a row vector is multiplied on the right by a 2x2 matrix, then the output is again in R"; such matrices are called linear transformations. 1. Find a linear transformation that rotates the plane R by a radians. That is, find a matrix T such that...
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
2. Let F be a field, n > 1 an integer and consider the F-vector space Mat,,n(F) of n × n matrices over F. Given a matrix A = (aij) E Matn,n(F) and i < n let 1 row,(Α-Σ@y and col,(A)-Žaji CO j-1 j-1 be the sum of entries in row i and column i, respectively. Define C, A EMat,,(F): row,(A)col,(A) for all 1 < i,j < n] C, { A E Matn.n(F) : row,(A) = 0 = col,(A) for...
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