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(b) Consider continuous-time signals xi(t) and x2(t) respectively given as (t +1 -1 <t<o x1(t) =...
5. Suppose that three random variables Xi, X2, and X3 have a continuous joint distribution with...
5. Suppose that three random variables Xi, X2, and X3 have a continuous joint distribution with the following p.d.f. (x1+2x2+3z3) and f(1, r2, 3) 0 otherwise. (a) Determine the value of the constant c; (b) Find the marginal joint p.d.f. of Xi and X3; (c) Find P(Xi < 1|X2-2, X3-1)
The joint density of random variables X1, X2 is given by fx1,x2 (x1, 2)= 6x1, for...
The joint density of random variables X1, X2 is given by fx1,x2 (x1, 2)= 6x1, for 0 < xı < 1, 0 2 <1 - r Let Y X1X2. Find the joint density of Yi and Y2 Х1, Y?
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 <...
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.
max Xi + 3x2 subject to: -X1 – x2 < -3 -21 + x2 = -1...
max Xi + 3x2 subject to: -X1 – x2 < -3 -21 + x2 = -1 X1 + 2x2 = 2 X1, x2 > 0 Problems. Solve the following problems using the simplex method in the dictionary form. Note that problems 2, 3, and 4, require you to use the two-phase simplex method. For each iteration, in addition to other calculations, clearly show the following: the dictionary, entering variable, minimum ratio, and the leaving variable. Note that we employ Dantzig's...
Signals and Systems 1. A continuous time system is given inputs x1(t), r2 (t), and x3(t), from which the outputs yi (t), y2(t), and y3( arise, respectively, where 1(t)u(t) u(t-1) i(t)2u(t) -e20-u(t -...
Signals and Systems
1. A continuous time system is given inputs x1(t), r2 (t), and x3(t), from which the outputs yi (t), y2(t), and y3( arise, respectively, where 1(t)u(t) u(t-1) i(t)2u(t) -e20-u(t - 1) 2(t)u(t) - u(t- 3 T3 0 otherwise sin(5t) te,1 y3(t) 0 otherwise e-5t (u(t)-a(t-1)) ya(t) = (a) Is this system causal? Prove your answer. (b) Is this system linear? Prove your answer. c) Is this system time-invariant? Prove your answer.
1. A continuous time system is...
Mathematical Statistics (1) Exercise6TROSS12⑥4, 276.29) alet X-(X1,X2) be a random vector with probability density function given...
Mathematical Statistics (1)
Exercise6TROSS12⑥4, 276.29) alet X-(X1,X2) be a random vector with probability density function given by (zi,T2) = 24x1x2 with support determined by 0 < xi + X2く1,21 > 0,x2 > 0. Determine each of the following. (i) fi(xı) (ii) f2(t2) (iii) E(X1%) (iv) E( %)
Problem 2 Consider a continuous-time LTI system whose frequency response is given by 2 sin(40 (a)...
Problem 2 Consider a continuous-time LTI system whose frequency response is given by 2 sin(40 (a) Find the impulse response, h(t) of the system (b) Determine the outputy() =x(t)*h(t) of the system given an input x(f)--1, ț < 8 4 otherwise 0,
Part A - Pre-work: 12 Marks) A.1 Consider the continuous-time signals given in Figure 1. al)...
Part A - Pre-work: 12 Marks) A.1 Consider the continuous-time signals given in Figure 1. al) b(t) -1 -1 -1 f(0) 9(0 Figure 1 Evaluate the following convolution integrals and sketch the results. a. a(t)8b(t) Signals and Systems (300057)Lab 4-Version 1.0
answer a and b only Suppose that two continuous time signal are given by x(t) and...
answer a and b only
Suppose that two continuous time signal are given by x(t) and v(t) as: x(t) = u(t) - 2u(t - 1) + u(t - 2) v(t) = u(t)- uſt - 1) Answer the following questions: (a) Plot signals x(t) and v(t). (b) Find the convolution of y(t) = x(t-3) = v(t) (c) Plot for y(t).
(2) 1-2 st 32 sec Given: xi(t) = {0 elsewhere and xz(t) = {o -2 st...
(2) 1-2 st 32 sec Given: xi(t) = {0 elsewhere and xz(t) = {o -2 st 32 sec elsewhere Use Fourier transform pairs/theorems to find the convolution z(t) = x1(t) * x2(t). Express your final answer in the time domain. (25 pts)
5. Suppose that three random variables Xi, X2, and X3 have a continuous joint distribution with the following p.d.f. (x1+2x2+3z3) and f(1, r2, 3) 0 otherwise. (a) Determine the value of the constant c; (b) Find the marginal joint p.d.f. of Xi and X3; (c) Find P(Xi < 1|X2-2, X3-1)
The joint density of random variables X1, X2 is given by fx1,x2 (x1, 2)= 6x1, for 0 < xı < 1, 0 2 <1 - r Let Y X1X2. Find the joint density of Yi and Y2 Х1, Y?
Exercise 7 (team 5) Let Xi and X2 have joint pdf x1 + x2 if0<x1 < 1 and 0 < x2 < 1 /h.x2 (x1,x2) = 0 otherwise. When Y1 X1X2 derive the marginal pdf for Y.
max Xi + 3x2 subject to: -X1 – x2 < -3 -21 + x2 = -1 X1 + 2x2 = 2 X1, x2 > 0 Problems. Solve the following problems using the simplex method in the dictionary form. Note that problems 2, 3, and 4, require you to use the two-phase simplex method. For each iteration, in addition to other calculations, clearly show the following: the dictionary, entering variable, minimum ratio, and the leaving variable. Note that we employ Dantzig's...
Signals and Systems
1. A continuous time system is given inputs x1(t), r2 (t), and x3(t), from which the outputs yi (t), y2(t), and y3( arise, respectively, where 1(t)u(t) u(t-1) i(t)2u(t) -e20-u(t - 1) 2(t)u(t) - u(t- 3 T3 0 otherwise sin(5t) te,1 y3(t) 0 otherwise e-5t (u(t)-a(t-1)) ya(t) = (a) Is this system causal? Prove your answer. (b) Is this system linear? Prove your answer. c) Is this system time-invariant? Prove your answer.
1. A continuous time system is...
Mathematical Statistics (1)
Exercise6TROSS12⑥4, 276.29) alet X-(X1,X2) be a random vector with probability density function given by (zi,T2) = 24x1x2 with support determined by 0 < xi + X2く1,21 > 0,x2 > 0. Determine each of the following. (i) fi(xı) (ii) f2(t2) (iii) E(X1%) (iv) E( %)
Problem 2 Consider a continuous-time LTI system whose frequency response is given by 2 sin(40 (a) Find the impulse response, h(t) of the system (b) Determine the outputy() =x(t)*h(t) of the system given an input x(f)--1, ț < 8 4 otherwise 0,
Part A - Pre-work: 12 Marks) A.1 Consider the continuous-time signals given in Figure 1. al) b(t) -1 -1 -1 f(0) 9(0 Figure 1 Evaluate the following convolution integrals and sketch the results. a. a(t)8b(t) Signals and Systems (300057)Lab 4-Version 1.0
answer a and b only
Suppose that two continuous time signal are given by x(t) and v(t) as: x(t) = u(t) - 2u(t - 1) + u(t - 2) v(t) = u(t)- uſt - 1) Answer the following questions: (a) Plot signals x(t) and v(t). (b) Find the convolution of y(t) = x(t-3) = v(t) (c) Plot for y(t).
(2) 1-2 st 32 sec Given: xi(t) = {0 elsewhere and xz(t) = {o -2 st 32 sec elsewhere Use Fourier transform pairs/theorems to find the convolution z(t) = x1(t) * x2(t). Express your final answer in the time domain. (25 pts)
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