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(57+7)+(2 +3 +4 k, where t o Find T1-1). (20) Consider the curver() NI-1) and B(-1)
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find...
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find the length of the curve from the point wheret = 0 to the point where t = 71 O 75.7 G O 7/3.7 2. O 7V2.7 2 7.T 2 3 (Recall questions 9-11 all ask about the same curve) Find the arc-length parametrization of the curver(t) = (cos(26), t, sin(2t)), measure fromt O in the direction increasing t. Or(s) = (cos(V28), V28, sin(28)) Or(s)...
Find the value(s) on the curver = 2 + 2 cos 0 where the tangent line...
Find the value(s) on the curver = 2 + 2 cos 0 where the tangent line is horizontal. 0 0 = 7, 1657 OD=7, 5, 116 00=T, 5, 00 = 0, 2, O 0 = 57,75 00= 0,
Consider k groups and considerYi,Y2...,Yk independent random variables, where Yi ~b(ni,P)1,2,.., k, Let ni be a...
Consider k groups and considerYi,Y2...,Yk independent random variables, where Yi ~b(ni,P)1,2,.., k, Let ni be a fixed value representing the number of items and Pi the probability that they respond to a fixed non-random covariate represented by di, di, d, d. Then we have, In 1-pi with parameters /o and A. Find a two-dimensional sufficient statistic for (Bo,B)
2. Consider a periodic signal shown below (20 points) i(t) -7 -6 -5 -4 -3 -2...
2. Consider a periodic signal shown below (20 points) i(t) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 (a) Find the fundamental period of this signal. (b) Consider following two signals, xi(t) and x2(t), obtained from the above signal, find their corresponding Fourier transforms: xi(t) -1 0 1 *2 (1) Its of, 0 1 2 3 4 5
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where...
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where x = 3t and y = 1 − t. (b) z = f(x, y, t), where x = a + bt, and y = c + k
14. (20 pts total) Consider the following cell reaction at 25 o°C: 2 Al(s)3 Ni (aq)>2...
14. (20 pts total) Consider the following cell reaction at 25 o°C: 2 Al(s)3 Ni (aq)>2 A (aq) +3 Ni(s) Calculate the following: a. (10 pts) Under standard conditions, calculate the Gibbs Free Energy, AG , in J. (Standard reduction potentials are in the last page of the exam) b. (10 pts) At non-standard conditions, if the concentrations of Ni respectively, calculate the E, in V. Assume T 25 °C. and Al are 0.015 M and 0.010 M,
(i) Consider the wave Ē(7,t) = Ło cos(wt – k ), where Ē, is a fixed...
(i) Consider the wave Ē(7,t) = Ło cos(wt – k ), where Ē, is a fixed vector. Determine the relation between w and k = \KI SO that Ē(7,t) is a solution of the wave equation -27 182 VPE = 2 ət? - What is the direction of propagation of the wave? ii) Show, by substitution of Ē(7,t) in the appropriate Maxwell's equation, that K· Ē= 0. iii) Assuming that the magnetic field B(7, t) = B, cos(wt – K:1),...
1) Consider a normal WSS process X(t) with E{X(t)3 - 0 and Xx b) E(lX(t1) -...
1) Consider a normal WSS process X(t) with E{X(t)3 - 0 and Xx b) E(lX(t1) - X(t -1)]2)
Problem 3 Consider the Gaussian process, X(t), with zero mean and a utocorrela- t ) i,2 tion function Rx(t1, t2 mini 1....
Problem 3 Consider the Gaussian process, X(t), with zero mean and a utocorrela- t ) i,2 tion function Rx(t1, t2 mini 1. Find the covariance matrix of the random variables X(1) and X (2) 2. Write an expression for the joint PDF of X(1) and X(2)
Problem 3 Consider the Gaussian process, X(t), with zero mean and a utocorrela- t ) i,2 tion function Rx(t1, t2 mini 1. Find the covariance matrix of the random variables X(1) and X (2)...
Consider T:R4 → R3 with 1 [T) 3 2 -4-1 0 0 5 7 8 10...
Consider T:R4 → R3 with 1 [T) 3 2 -4-1 0 0 5 7 8 10 4 3 -20 -6 1 0 0 5 om Find a basis for image(T). What is dim(image(T))? Convert image(T) to relation form.
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find the length of the curve from the point wheret = 0 to the point where t = 71 O 75.7 G O 7/3.7 2. O 7V2.7 2 7.T 2 3 (Recall questions 9-11 all ask about the same curve) Find the arc-length parametrization of the curver(t) = (cos(26), t, sin(2t)), measure fromt O in the direction increasing t. Or(s) = (cos(V28), V28, sin(28)) Or(s)...
Find the value(s) on the curver = 2 + 2 cos 0 where the tangent line is horizontal. 0 0 = 7, 1657 OD=7, 5, 116 00=T, 5, 00 = 0, 2, O 0 = 57,75 00= 0,
Consider k groups and considerYi,Y2...,Yk independent random variables, where Yi ~b(ni,P)1,2,.., k, Let ni be a fixed value representing the number of items and Pi the probability that they respond to a fixed non-random covariate represented by di, di, d, d. Then we have, In 1-pi with parameters /o and A. Find a two-dimensional sufficient statistic for (Bo,B)
2. Consider a periodic signal shown below (20 points) i(t) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 (a) Find the fundamental period of this signal. (b) Consider following two signals, xi(t) and x2(t), obtained from the above signal, find their corresponding Fourier transforms: xi(t) -1 0 1 *2 (1) Its of, 0 1 2 3 4 5
14. (20 pts total) Consider the following cell reaction at 25 o°C: 2 Al(s)3 Ni (aq)>2 A (aq) +3 Ni(s) Calculate the following: a. (10 pts) Under standard conditions, calculate the Gibbs Free Energy, AG , in J. (Standard reduction potentials are in the last page of the exam) b. (10 pts) At non-standard conditions, if the concentrations of Ni respectively, calculate the E, in V. Assume T 25 °C. and Al are 0.015 M and 0.010 M,
(i) Consider the wave Ē(7,t) = Ło cos(wt – k ), where Ē, is a fixed vector. Determine the relation between w and k = \KI SO that Ē(7,t) is a solution of the wave equation -27 182 VPE = 2 ət? - What is the direction of propagation of the wave? ii) Show, by substitution of Ē(7,t) in the appropriate Maxwell's equation, that K· Ē= 0. iii) Assuming that the magnetic field B(7, t) = B, cos(wt – K:1),...
1) Consider a normal WSS process X(t) with E{X(t)3 - 0 and Xx b) E(lX(t1) - X(t -1)]2)
Problem 3 Consider the Gaussian process, X(t), with zero mean and a utocorrela- t ) i,2 tion function Rx(t1, t2 mini 1. Find the covariance matrix of the random variables X(1) and X (2) 2. Write an expression for the joint PDF of X(1) and X(2)
Problem 3 Consider the Gaussian process, X(t), with zero mean and a utocorrela- t ) i,2 tion function Rx(t1, t2 mini 1. Find the covariance matrix of the random variables X(1) and X (2)...
Consider T:R4 → R3 with 1 [T) 3 2 -4-1 0 0 5 7 8 10 4 3 -20 -6 1 0 0 5 om Find a basis for image(T). What is dim(image(T))? Convert image(T) to relation form.
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