Find the value of 8dc 22 +1 0 00 Determine whether 8 n2 + n=1 is a convergent series. Enter C if series is convergent, D if series is divergent. C Show work here by typing it or attaching a file or picture
Express the following limit as a definite integral: 22 3i lim n-+00 2522 n2 1 n2 i=1
Suppose X, Y are independent with X ∼ N (0, 1) and Y ∼ N (0, 1). Show that the distribution of Q = X/Y follows the Cauchy distribution, i.e., f(q) = 1/π(1+q2) . Hint: Let Q = X/Y and V=Y. Find the joint pdf of Q and V and finally find the marginal pdf of Q by integrating the joint pdf of Q and V w.r.t. V: Y π(1+q2) Y V = Y . Find the joint pdf of...
(x - 2)" dn=0 n2 1
(x - 2)" dn=0 n2 1
u(x,0)= Consider the following wave equation U, = U23 -00<x<00,t> 0 (0, -0<x<-1, _x+1, -1<< <0, 1-x, 0<x<1, 1<x<00 (0, -00<x<-1, u,(x,0) = 1, -15xs1, (0, 1<x<0. Find u(1,0.5) and u(-1,0.5).
If f(x) := {n=0 (-1)"x" 3” n2 for x € (-3, 3), find f(100) (0). Hint: use the coefficients in Taylor's Theorem to solve for the required derivative, and invoke the uniqueness of power series with given centers (proved in Thursday's lecture). Or, take the first couple derivatives, evaluate them at r = 0, and find the pattern.
I. (a) Compute g(x) = £ (n2 +n)x”. (b) Compute E (n?+n)/2". Justify your method. n=0 n=0
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
Find the series' radius of convergence. (x-6) 1) An +2 Σ n=0 00 (x-gn 2) M n=1
How is the last step done done
N-1 3 i⅔n2 e 10 10 N _ n-0
N-1 3 i⅔n2 e 10 10 N _ n-0