Question 2 (BN 4.11) Fix a with 0 < a < i. Let g(t) = 1-t2 for a and 0 otherwise. t < 1 Discretize g over [0, 1 with 7. Plot the magnitudes of the level-6 wavelet coefficients. Estimate...
2te-t2 { 2te-1 = t> 0 6. Let g(t) be the probability density function of the continuous 0 t < 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that P(X <m) = } = 0.5. [7]
2, let f(t)-〈 2t 2-t < 4 ; g(t) = . 0 otherwise 0 5<t (a) Write each function in terms of the unit step fun ction (b) Plot each function (c) Find the Laplace transform of f (t) and g(t) 2, let f(t)-〈 2t 2-t
Let gx)- t) dt, where f is the function whose graph is shown (a) Evaluate gtx) for x - 0, 1, 2, 3, 4, 5, and 6 gt1)-1/2 0t2)-0 g(3) - -1/2 ot4)-0 9(5)-3/2 9(6)-4 (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimumx maximum x (d) Sketch a rough graph of g. Let gx)- t) dt, where f is the function whose graph...
Question 7 (Chapters 6-7) 2+2+2+3+2+4+4-19 mark Let 0メs c Rn and fix r' E S. For a R" consider the following optimization problem: (Pa) min ar res and define the set K(S,) (aER z" is a solution of (Pa)) (e) If z' e int(S), prove that K(S, (0) (1) If possible, find a set S CR" and s* E S such that K(S,) (g) Let SB, 0.1] (rR l2l3 1) (the closed (, unit ball) and consider (1,0)7. Prove that...
0.09/1 points Previous Answers SCalcET8 5.3.002. Let g(x)-f(t) dt, where f is the function whose graph is shown (a) Evaluate g(x) for x 0, 1, 2, 3, 4, 5, and 6 g(0)0 9(2)-8 g(3)-( 20 9(4)- 9(5) 9(6) ) g(6)- (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimum x= maximum x= (d) Sketch a rough graph of g. 7 83 gtx ry again....
Signal and system (I already have solution pls plot the function) Question 2: Let Zi (t) = Σ00-oo akejinkt and let x2(t) = Σ00-00 bkejinkt. Here assume ak 〉 0 yk and that Compute and plot y(t) Solution: Here we have perio k, when |k| = 1 and bk - o otherwise. Further define y(t) - 17i(T)x2(t -T)dT d T = 1 and W-2T. Now y(t) = 11-1(T)22(t-T)dr bkw dr (Substituting for r2(t -T) T1 (T =ibeekut (1hzī(r)e-jk."dr) (Interchanging sum...
Example 8.5.1. Let if 0< x< T if 0 or r? -1 if -т <т < 0. 1 f(x)= 0 _ The fact that f is an odd function (i.e., f(-x) = -f(x)) means we can avoid doing any integrals for the moment and just appeal to a symmetry argument to conclude T f (x) cos(nar)dx 0 and an f(x)dax = 0 ao -- T 27T -T for all n 1. We can also simplify the integral for bn by...
Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E ] 5. V i 6. V i 7. E ( E) 8. E Construct the LR(0) DFA for this grammar a) b) Construct the LR(0) parsing table. Is it LR(o)? Why and why not? Let G be the following grammar: 1. S T 2. T O 3. T T 4. O V = E i [ E...
Question 8 (Chapters 6-7) 12+2+2+3+2+4+4-19 marks] Let 0メS C Rn and fix E S. For a E R consider the following optimization problem: (Pa) min a r, and define the set K(S,x*) := {a E Rn : x. is a solution of (PJ) (a) Prove that K(S,'). Hint: Check 0 (b) Prove that K(S, r*) is a cone. (c) Prove that K(S,) is convex d) Let S C S2 and fix eS. Prove that K(S2, ) cK(S, (e) Ifx. E...
• Question 16 B0/10 pts over the interval [2, 7) using ten approximating Estimate the area under the graph of f(x) = rectangles and right endpoints. Rn = Repeat the approximation using left endpoints. Ln = Report answers accurate to places. Remember not to round too early in your calculations. Question Help: Video Submit Question . Question 13 B0/10 pts 498 OD When estimating distances from a table of velocity data, it is not necessary that the time intervals are...