Consider a market where X is a continuous semimartingale. Define the trading strategy (Vo. ) by vo 5, ,2(X, +1) Find Gr...
Consider a market with X W, where W is a Brownian motion process. Define the trading strategy (Vo. ) by vo 1, ,2W Find Gr(p) Select one: WA-T 2WT W2+T
Consider a market with X W, where W is a Brownian motion process. Define the trading strategy (Vo. ) by vo 1, ,2W Find Gr(p) Select one: WA-T 2WT W2+T
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 1W -, 0sIST Then p, is equal to Select one: tW 2W W2 W
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 1W -, 0sIST Then p, is equal to Select one: tW 2W W2 W
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 3+ W3 -3rW, 0 IST. Then p, is equal to Select one: W, W2 3W2-3t - t 3+W
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 3+ W3 -3rW, 0 IST. Then p, is equal to Select one: W, W2 3W2-3t - t 3+W
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 1W -, 0sIST Then p, is equal to Select one: tW 2W W2 W
Consider a market with X W, where W is a Brownian motion process. Consider the trading strategy (Vo. ) with value V, 1W -, 0sIST Then p, is equal to Select one: tW 2W W2 W
X with density fcx)3/56 ir 2<<4 5. Consider a continuous random variable X with density f(x)- otherwise a. Find P(1 <X<3) b. Find ECX)
consider continuous joint density function f(x,y)= (x+y)/7; 1<x<2, 1<y<3 Marginal density for Y? Select one: (2+3x)/14 (3+2y)/7 (2+3y)/14 (3+2y)/14 consider continuous joint density function f(x,y)= (x+y)/7 ; 1<x<2, 1<y<3 P(0<x<3, 0<y<4)=? Select one: 0.5 1 0.15 0.25
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
1. Consider rolling two fair, six-sided dice, and define the RV X to be the minimum of the two values you get. E.g. if s (2,5) then X(s) = min{2,5} =2. (a) (2 points) What are the possible values of X? (b) (2 points) Find the probability P(X 1) (c) (2 points) Find the probability P(X 3) (d) (4 points) Find the probability P(X 5) 2. Consider 3 events A, B, C, together with their associated indicator RV's IA, IB,Ic...
(6 marks) Consider a filtered probability space (2,F,P, Ftte.). a. (2 marks) Let the stochastic process (Xo.7] have independent increments and sat- b. (2 marks) Let eo.] be a stochastic process with Ep[X] Xo for all t E [0,T]. Is c. (2 marks) Let (W be a Brownian motion. Given c 0, and define the stochastic isfies Ep[IXll < oo fort [0,T]. Is the stochastic process {Ztieo.r], where z, = xt-EP[Xt] is a martingale with respect to {Ft}120 ? Explain....
13. Let X be a continuous random variable with density P(X0)0.3 and P(X 1) 0.7. Find (i) 1 - Fx(t) where Fx(t) is the cumulative distribution function of X (i) 1-Fx (t) da (iii) 0-P(X = 0) + 1 . P(X = 1) 0