Q1: If X and Y are jointly continuous random variables with probability density function f(x,y) given by f(x, y) 3)= {(x + 1) (x+y) 0≤ x ≤1 and -1 ≤ y ≤ 1 otherwise a. Compute Cov(X,Y). b. Compute the correlation (pxy) between X and Y. c. Are X and Y independent? Note, show the steps of your solutions.
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Q: 2. Simplify the Boolean functions K-map. a. F (w, x, y, z) = Σ (0, 1, 2, 4, 5, 6, 8, 9, 12, 13, 14)
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Q: 4 - variable K-Map, the cells (0,1,2,3,8,9,10,11) can be grouped
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- Gaussian white noise X(t) with power spectral density of 1 passes through two band-limited filters H₁(jw) and H₂(jw) respectively, and the output is Y₁(t) and Y₂(t) respectively. (a) The mean values of Y₁(t) and Y₂(t) and the self-power spectral densities are given (b) Calculate the mutual power spectral density of Y₁(t) and Y₂(t)3.10 The random variable X has the probability density function | 2x, 0Could you please help me with the highlighted question at the bottom please?Consider the following continuous time system that sums two input signal z1(t) and z2(t) with aj and az weights respectively, and gives output signal as y(t) = ajz1(t) + agr2(t). If z1(t) = 2+ cos(6xt +x/4), and ra(t) = 1+ cos(2nt – n/4). a)r Determine and express the Fourier series representation of z (t) signal along with its coefficients ap. b). Determine and express the Fourier series representation of ze(t) signal along with its coefficients by. c . Determine and express the Fourier series representation of y(t) signal along with its coefficients C . d) el Determine and explain how to find the fundamental frequency of y(t) signal. Maximum size for new files: 100MB, maximum attachments: 1Q2) Consider the signal given below. 1 xx(t) O 2 3 5 a) Determine energy density function e(f) of x(t). b) Determine the energy E, of the signal. t(sec)Problem 2 Given: f(W,X,Y,Z) = Em(4,5,7,9,10,15) + Ed(2,6,11,13) In consideration with the most economical design of the circuit, simplify the given Boolean function f in Sum-of- Products (SOP) form with Don't-Care conditions. Note: Show the necessary map to support your answer. Appropriately label all groups on the map. Show all grid lines on map.Suppose Y is a continuous random variable drawn from the uniform distributionon the interval [3, 4], that is, Y ∼ Uniform([3, 4]). Conditioned on Y = y, a second randomvariable X is drawn from the uniform distribution on the interval [0, y]. What is fX(x), thepdf of X?Signals and systemsA continuous random variable X had a pdf shown below. Find (A) K, and (B) P{X>1). K(2x-x²) 0x(1) Q1: For the continuous-time signal x(t) shown in Fig.1: a- Sketch x(-21). 3 b- Sketch x(t/3). c- Sketch x(-47+4). -2 Fig.1 d- Find and sketch the even part of the signal x(1). e- Find and sketch the odd part of the signal x(t). 4.s). By the DFT definition we have Y = WNy where y(0) y(1) Y (0) Y (1) y = Y = Ly(N – 1)] [Y(N – 1)] 1 1 1 1 WN WN-1 1 WN W w2(N-1) 1 WN N 7(N-1) 72(N-1) w(N-1)(N-1) Find W3 and the DFT of y(n) = {-3, 1, –2}.Consider DFT of two real sequences as a result from the given functional form x1 (n) and X2(n). Compute its frequency co-efficient X, (k) and X,(k) if the input samples are: 0Recommended textbooks for youIntroductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationFundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationFundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,