You must show your work clearly!!!
You must show your work clearly!!! Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one: t2 3 2t 3 x 2t Let W W t0) be a Brownian motion. Find E(W (W14 t+4 Wt15)): Select one:...
{ W, : t > 0} be a Brownian motion. Find E(W, (W2t --We), where 0 < t < 1: Let W Select one: t (1 -t) 0 { W, : t > 0} be a Brownian motion. Find E(W, (W2t --We), where 0
4. [20 points] Let {B(t):t0 be a standard Brownian motion. Define a stochastic process (X (t):t20) by the formulas X (t) = tB(1 + t-1)-tB(1), x(0) = 0, t > 0, You may take for granted the fact that imt-«HX(t) = 0, with probability 1 (b) Explain why [X():t20 is a standard Brownian motion 4. [20 points] Let {B(t):t0 be a standard Brownian motion. Define a stochastic process (X (t):t20) by the formulas X (t) = tB(1 + t-1)-tB(1), x(0)...
3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B Find functions g and h such that X, has the same covariance as a Brownian bridge. 3. Let U-Bt- tB be Brownian bridge on [0, 1], where {BiJosesi is a Brownian process (i) Show E(Ut0 (ii) Show Cov(U,, Ut) s(1- t) for 0 s ts1. (ii) Let Xg(t)B...
Let f(t) = t? and g(t) = 2t + 3. Find f*g. Select one: 1 t4 +3t3 12 123 a. 1 b. t +t3 1 +4 +t3 + 3t? 12 *** +++ Type here to search
Find f. f'(t) = 2t - 4 sint, (0)= 5 Select one: a. f(t) = 2t - 3 sint +5 O b. f(t)= +2 +4 cost +1 c. f(t)=12 - 3 cost-5 d. f(t) = x2 +3 cost e. None of these
2. Let Mx(t) = 1c' + 2t?c". Find the following: (b) Var(X). (c) If Y = X-2, show that the moment-generating function of Y is e-2tMx(t). (d) If W = 3X, show that the moment-generating function of W is MX(3). 7/3,5/9
Question 4 (2 marks) Attempt 3 f(t)--t Find the Fourier transform of: e-10t 16-+t2)2 Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) = Question 4 (2 marks) Attempt 3 f(t)--t Find the Fourier transform of: e-10t 16-+t2)2 Your answer should be expressed as a function of w using the correct syntax. Fourier transform is F(w) =
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
LINEAR ALGEBRA, please show all your work and clearly circle answer. thank you! 3, 4 3. Two fair dice are rolled, one red and one green, and the numbers on the top faces are noted. Let event E be "red number is 3 or 4 or 5" and event F be "sum is 10 or higher." Are E and F independent or dependent? 4. Bag 1 contains four red and five blue marbles, and Bag 2 contains two red and...
1,2 and 3 Directions: You must show ALL of your work as clearly as possible in order to receive full credit. If there is no enough space, please do your work on separate sheets of paper and staple them behind this worksheet. lim 1. (2 pts) Evaluate the limit n n° +5n 5n' + cos(n)+n 2. (4 pts) Show that the series n' +2n +1 231° +7 diverges. 3. (4 pts Determine whether the series is convergent or divergent 1...