9. [20 pts.] Recall that 1 +tAk.. 1 etA I+tA+tA2 2! k! (a) Compute e4 explicitly...
(b) Let X(ju) denote the Fourier transform of the signal r(t) shown in the figure x(t) 2 -2 1 2 Using the properties of the Fourier transform (and without explicitly evaluating X(jw)), ii. (5 pts) Find2X(jw)dw. Hint: Apply the definition of the inverse Fourier transform formula, and you can also recall the time shift property for Fourier Transform. (c) (5 pts) Fourier Series. Consider the periodic signal r(t) below: 1 x(t) 1 -2 ·1/4 Transform r(t) into its Fourier Series...
[20 total pts) Consider the sequences x1n] = { 1, 2,-2, 1}, and x2 [n] = { 1, 2,-2, 1, 0, 0, 0, 0). The sequence x2In] is known as a zero-padded version of x,[n]. When answering the questions below, please use Table 1, provided on Page 3. a. [3 pts] Compute X1(eo), the Discrete-Time Fourier Transform (DTFT) of x1 [n], and evaluate it for the following values of normalized frequency: a-63 笎哮,쯤뀨 write the values in the table b....
need help with #3
L. (3Upts) Consider the following ivp I)(24), 2(0) = 1.5. ut show that this ivp has a unique solution that exists everywhere on (-00, oo). Sk etch the graph of this solution with explanations (monotonicity, concavity,..) ow that the following initial value problem has a unique solution that exists for all t. cos(a) cos(et), a" +sin(a") cos(a') i r(0)-1, r"(0) = 0 . 4. (30 pts) Consider the following ivp r, y, 2x + y +...
K-means clustering Problem 1. (10 pts) Suppose that we have the gene expression values for 5 genes (G1 to G5) under 4 time points (t1 to t4) as shown in the following table. Please use K-Means clustering to group 5 genes into 2 clusters based on Euclidean distance. Find out the final centroids and their affiliated genes. The initial centroids are c1=(1,2,3,4) and c2=c(9,8,7,6). Please write down your algorithm step by step. Result without steps won't get points. t1 t2...
PLEASE ANSWER ALL OF THE QUESTIONS
Question 1 1 pts Each of three objects has a net charge. Objects A and B repel each other. Objects B and C attract each other. Which one of the following table entries is a possible combination of the signs of the net charges on these three objects? A B с (1) + + - + (2) + + (3) (4) - (5) + - 0 1) 3) 0 (3) and (5) O (1)...
4. (5 pts) Consider the sequence +2+12rk for k 2 0. Starting with an initial rmula for rk in term s of , compute z" by finding a general f condition 20 = 0, 띠 = 1 initial conditions
4. (5 pts) Consider the sequence +2+12rk for k 2 0. Starting with an initial rmula for rk in term s of , compute z" by finding a general f condition 20 = 0, 띠 = 1 initial conditions
Step by step for #8
1) Given (1 2 3 1 0 11 1 5 2 1 A= -2 -5 -4 -1 1 ( 3 5 11 4 1 Find the basis and dimension for the row, the column spaces, and the null space NA Also, state the rank, the nullity of A 2) The subspace of W in R spanned by vectors u =(2.-2.1) v =(1,2,2) is a plane passing thru the origin. Express the vector w=(1,0.2) in the...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Stella Mars Polyte Mo 404 (Probahlty and Statsti Exam (40 poiats) all st D t o The ve distl ta f de i X (2 pts)What is PIX1/2 7 a p) Wht P/2 a/2 iSpts) Whiat is the prohability deasity function of the1audn variable whoe cdf is Fi) T LXbe it zandom vairiable with proability density ftion ot w t What is the valui of C 2tsl What is fhe rumalatjve distnibution of X oI Let X he a toitinnous...
True or false?
Question 6 1 pts Every prime number other than 2 can be expressed in the form of 4k + 1 or 4k – 3 for some k E Z. True False Question 8 1 pts Suppose that algorithm A has running time na + 10 log2 (n) and the algorithm B has the running time n log2 (n) + 5n (where both depend on the input value n). Then for a sufficiently large input value n, algorithm...