1. Consider y(t) = Sant – 7)e(r)dr, -20 <t<oo. Compute y(t) given: z(t) = 6(t)e- -...
2. Let f(x,y) = e-r-u, 0 < x < oo, 0 < y < oo, zero elsewhere, be the pdf of X and Y. Then if Z = X + Y, compute (a) P(Z 0). (b) P(Z 6) (c) P(Z 2) (d) What is the pdf of Z?
in each case: (e) Compute y = sin(z)cos(r) for 0 < z < π/2
Find the Peano range of the Cauchy problem. Z=38 {r' = (2 = (Z -t)y,-3<t< 3; y(1) = 2
Question 3 1 pts Let 7 = (xy, - xy) and let D be given by 0 < x <1, 0<y<1. Compute Sap Ē. dr. 0-1 OO O1 O2
5. (2+2+3 Points) Consider the linear wave equation for-oo <エ<oo,-oo < t <oo for - oo<<oo for utt-c2uzz = f(x, t) tr(r,0)- (r) _oo < x < oo. a. Sketch the domain of dependence of the point (,t) (4, 1) in the (x, t)-plane in 1. case c = 2, Do the same in the case c b. State the general solution forrnula for this problem! in terms of the data f, φ, ψ. c. Now suppose ψ = 0...
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
Find solution to the IBVP PDE BCs Ic u(0, t)-0, 0<oo l u(1, t) 0, 0<t< oo u(z,0)=x-x2ババ1
Problem 5. The joint density of X and Y is given by e" (z+y) fx.-otherwise. İf 0 < x < oo, 0 < y < 00, Consider the random variable Z-; a) Find the cumulative distribution function of Z b) What is the probability density function of Z?
3) Given vector field F(x,y,z)=<y, xz,x? >. Find N dr where T is the path around the triangle with vertices (1,0,0),(0,1,0) and (0,0,1) traced counterclockwise (when viewed from above.)
Question 7 Given vectors u = <2, 1> and v= <3,4> to compute (a) u + v (b) - (c) u-30