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3. Let xn] -1, 0,1,2, 3,4,4,4,4,4) (a) Determine the sequences x[--n], x{n 3], and xn 21...
What’s the answer for (a) and (b) using Matlab?
Problem 1: Consider the following sequences x(n) = {-4, 5, 1,-2,-3, 0, 2, 45),-35ns4 y(n) = {6,-3,-1, 0, 8, 7,-2).-Isn 5 n(n) = {3, 2, 2,-1, 0,-2,5), 2sns8 The sample values of each of the above sequences outside the ranges specified are all zeros. Generate and plot the following sequences using MATLAB functions (c.g SIGSHIFT, SIGADD, fold, shift, etc.): (a) u(n) = x(n) + y(n-2) (b) s(n) =-y(n) + w(n +...
8. Let {Xn, n = 1, 2, . . . } and (, , n = 1, 2, . . . } be two sequences of random variables, defined on the sample space Suppose that we know . Xn → X, G.8 Prove that XnYX+Y.
8. Let {Xn, n = 1, 2, . . . } and (, , n = 1, 2, . . . } be two sequences of random variables, defined on the sample space Suppose that...
3. Let Xi, . . . , Xn be random samples of X and X(1), . . . , X(n) ordered random samples of X which are obtained from a rearrangement of X1,... , Xn such that (a) Show that the empirical distribution functions of Xi,..., Xn and Xo),..., X(n) coincide. (b) Consider the samples taken from X ~ F. Use (a) to compute A-2), F,,(-1)Ћ,(1.8),Ћ,(25) (c) (Continued from (b)) Plot A,(z) over-2 4.
Using the basic developed MATLAB signal functions, generate the following sequences and then plot the signal samples using the stem function. x_1[n] = 3 delta[n + 2] + 2 delta[n] - delta[n - 3] + 5 delta[n - 7], for -5 lessthanorequalto n lessthanorequalto 15. X_2[n] = 10u[n] - 5u[n - 5] - 10u[n - 10] + 5u[n - 15]. Generate the periodic sequence and plot the samples (using the stem function) of cap x[n] = {..., -2, -1, 0,...
2. A system is described by the following difference equation n]1.5y[n0.56y[n -2]+x{n-0.2x{n-] a) Find the transfer function of the system b) Let xn]un]. Compute an analytical expression for the response y[n]. Use Matlab to calculate the coefficients c) Simulate and plot the response using Matlab.(stem plot) Generate 50 points. (Matlab: x ones(1,50));
2. A system is described by the following difference equation n]1.5y[n0.56y[n -2]+x{n-0.2x{n-] a) Find the transfer function of the system b) Let xn]un]. Compute an analytical expression for...
5. Let X n 2 0} be a Markov chain with state space S = {0,1,2,...}. Suppose P{Xn+1 = 0|X,p = 0 3/4, P{Xn+1 = 1\Xn, P{Xn+1 = i - 1|X, 0 1/4 and for i > 0, P{X+1 = i + 1|X2 = i} i} 3/4. Compute the long run probabilities for this Markov chain = 1/4 and =
& Let Yn = ao Xn ta, x n- do xn + a, Xn-1 ; n =1,2,... where Xi are iid RVs u ; n = 1, 2, with equal moon o and va siance 2.1 95 { yn in 21% SSS? Is {Yn: n 21 } WSS?
5. Let {xn} and {yn} be sequences of real numbers such that x1 =
2 and y1 = 8 and for n = 1,2,3,···
x2nyn + xnyn2 x2n + yn2 xn+1 = x2 + y2 and yn+1 = x + y .
nn nn
(a) Prove that xn+1 − yn+1 = −(x3n − yn3 )(xn − yn) for all
positive integers n.
(xn +yn)(x2n +yn2) (b) Show that 0 < xn ≤ yn for all positive
integers n.
Hence, prove...
Let Xn be a Markov chain with state space {0,1,2}, the initial
probability vector and one step transition matrix
a. Compute.
b. Compute.
3. Let X be a Markov chain with state space {0,1,2}, the initial probability vector - and one step transition matrix pt 0 Compute P-1, X, = 0, x, - 2), P(X, = 0) b. Compute P( -1| X, = 2), P(X, = 0 | X, = 1) _ a.
3. Let X be a Markov chain...
Let X be distributed as N(0, 1). Define Xn (1)"X, n 1,2, a. [3 pts] Show that Xn-X. b. [3 pts] Show that Xn -» X