t X(t), t2 0; denotes the Brownian motion process with drift and variance parameters, μ do2, respectively. Then prove that Var (X(t) - X(0)) = to² as the time unit A → 0.

Q: Find dy/dx for y = J_1P+4 t2 dt t2+4 X. 3

A:

Q: d lr()||] = ||F"(t)|| dt O True O False

A: Counter example: Let rt=t, 1, 0. This implies that, rt=t, 1, 0rt=t2+12+02=t2+1ddtrt=2t2t2+1=tt2+1…

Q: Let A(x) = 4 3 2 1 y f(t) dt for f(x) in the following figure. y = f(x) 1 2 3 4 Calculate A(0.5),…

A:

Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: S f (t) dt = cos(t²) + C, what is f (t)?

A: Given query is to find f(t).

Q: Suppose that f is a function defined as f(r) = | (+4)dt . Find each of the f(1) = f(x) = f'(r) =

A: Answer and explanation is given below

Q: where a = If loga z= dt, then r= exp

A:

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: X = W;Wt-1 || Whether is strictly stationary or Wt not with to be mean zero Gaussian white noise…

A: GivenXt=WtWt-1where Wt is Gaussian white noise process. So mean is 0 and its variance is σ2. Xt is…

Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

A:

Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: 2t If X has moment generating function M (t) = the E (X) is equal to 1+3t

A:

Q: 2.Use the Fundamental Theorem of Calculus Part 1 to find the derivative of the functions 17 yt a)…

A:

Q: Suppose f(x) = [ 6t² /1+t° dt .

A:

Q: find 1 :-1 I(s) = [ds| In| r(2)= fdt e* t= I(2):

A:

Q: Solve for P(t) using the given information. d² p dt² = (6t, 2+3t), P(1)=(2,1), P'(1)=(3,2)

A: We have to solve given Questions.

Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: Use the chain rule to find dz dt || dz dt z = sin(x) cos(y), x = √t₁ y = ²/

A:

Q: Suppose f = f(g, h), g = g(t), and h = h(t). Find df/dt when t = 2, given the following. g(2) = -9,…

A: We have to find value of df/dt at t=2

Q: Let F(x) = dt . Then (t + ¢8j19 F'(x) =

A:

Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: 3. Let G(x) = fi (1? – 2) dt. Calculate G(1), G'(1), and G'(2). Then find a formula for G(x).

A: Both upper and lower limits are same, therefore G(1) = 0