Let W denote a standard Brownian motion and define Is X(t) a martingale? X(t) = e(t).

Q: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

A: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Find G'(w) if G(w) = 9 6 4w +6+ √w.

A:

Q: Yt = €t – 0.5ɛt–1 + 0.5€t-2 Et ~ WN (0, 1) (a) Find E(y) and Var(y.). (b) Find Cor(yt, Yt–1) and…

A: We have to use definition of stationary time series.

Q: Let y(t)= r(t)-2r(t-1)+r(t-3)+u(t-4), where r(t) is the ramp function. a) plot y(t) (10 pts.) b)…

A: The objective of the question is to plot the function y(t), z(t) and y'(t) and calculate the energy…

Q: Let Y have the pdf fy (y) = Let U e-Y. Find the pdf of U. = = e-y (1+e-y)2¹ -∞ <y<∞.

A:

Q: Which of the following functions (y1, y2) is a Lyapunov function for the dynamical system y₁ = - Y₁…

A: Which of the following function Vy1 , y2 is the Lyapunov function for the dynamic system? y1˙=-y1y22…

Q: dy in terms of t: Differentiate parametrically to find dx y= 2t2 +4 t - 1 X = A [4t(t – 1)²] В…

A: Given :x=1t-1y=2t2+4

Q: ( + The oscillation of a spring-mass system is determined by u" + 2u = 0.Which of the following…

A:

Q: At what point (s) does the curve : z = x² + y²? r(t) = ti+ (3t - t²) k intersect the paraboloid

A: We have to find the point on which the curve intersect the paraboloid

Q: b) If B¿ is standard Brownian motion, then P(B, > 2) = P(B1< -2). P(B < -2). %3D

A: To find true or false for the given statement.