Let W(t) be the standard Brownian motion, and let X(t) = t W(1/t) for t > 0, X(0) = 0. Show that the covariance (Cov) function of X(t) is the same as the covariance function of W(t): Cov(X(t); X(s)) = Cov(W(t); W(s)) for all s; t > 0. Assuming that the paths of X(t) are continuous with probability 1, argue that X(t) is standard Brownian motion?

Q: Calculate the sign Svsb(t) for the sign m(t). Calculate the bandwidth of the VSB signal. Calculate…

A: VSB stands for vestigial side band modulation. It is a type of amplitude modulation mainly used in…

Q: Are x, sin(x) and cox(x) linearly independent

A: True x, sin(x), cos(x) are linearly independent

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: Consider any(n) + an-1y(n-1) + + a1y' + aoy = f(x) where an, ...a1, ao E R, where an 7 0. ... (a)…

A: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

A:

Q: f(x)=cos(x), on [0,2π). solve f(x)=0

A: Given query is to find the Indicated angles .

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: Let x (t) =y(t) +sin(t), x2(t)=y (t) then x2(t)= x,(t)- cos(t) Select one: O True False

A: given x1(t)=y(t)+sin(t) , x2(t)=y'(t)

Q: Let f"(t) = /t – 2 cos t. Determine a general f(t). -

A: Given : f'''t = t - 2cost

Q: (r,1) = (r sin (f), r– cos (1)), (r.1) = (5,-) s numbers in exact form. Use symbolic notation and…

A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: calculate r'(t) and T(t), and evaluate T(1). r(t) =〈cos πt,sin πt,t〉

A: Given :                   r(t) = cos πt , sin πt , tDifferentiating with respect to t, we get…

Q: Let u(æ) = sin(x) and v() = a = 18 and f(x) (*)a u (2) -| v (2) = u'v – uv f'

A:

Q: Compute the Jacobian for the substitutions x = p sin cos 0, y = p sin Ø sin 0, z = p cos 0.

A: Step 1: Step 2: Step 3: Step 4:

Q: Let 7'(t) = (3+ 4t, cos(t), 6e*) and F(0) = (7, 2, 5). Determine 7(t). †(t) = (, , )

A:

Q: Q2):- Find Y[Z] of signal Y[n]=(Cos wn). U[n]

A:

Q: Make the orthagonal set of functions {1, cos(x), cos(2x), ...} orthonormal on the interval [0,2pi].

A: Two distinct functions f and g are said to be orthogonal on [a,b] if <f,g>=0   , where < ,…

Q: Find a potential function for F or determine that F is not conservative. F = (cos(z), 16y, -x…

A: The vector field given in the question is: F = <cos(z), 16y, -xsin(z)> Hence, F1 = cos(z), F2…

Q: Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subparts.

Q: Consider f : R and g: R- differentiable functions. Suppose that D (g(x)) is a matrix whose rows are…

A:

Q: Img(:)=v(x.y) and g(-)=g: v(x, y) = 2x-2ry+sin xsly and g (0)=-1.

A:

Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r – cos (t)), (r, t) = ( 6,…

A: Jacobian of the function at a given point

Q: Let f(z) := z5 . Show that f is invertible in a neighbourhood of i and calculate (f-1)'(f(i)).

A:

Q: Let f(z) = cos and g(z) = tan-(10z) Then if h(z) S(z) find: 9(z) h'(1) = N(즉) = |

A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

A:

Q: Find the derivative matrix for the functions at the given points. Then find f o k; (s0,t0)=(1,1). a)…

A: Let us first write the definition of the derivative matrix for the functions at the given points.

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

A:

Q: Check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]

A: We need to check if y = sin(t)et is a solution to: d2y/dt2 + dy/dt = et[3cos(t) + sin(t)]. We have y…