1) In the balanced Y-Y circuit shown below, let Van=990<0° V (rms) and the load impedance per phase be Zy=60+j35 2. Find the complex power, apparent power, average power, and reactive power of the load (25 marks) 110 os os
Given the circuit in Figure 8.6, find vc(t) for all t>0. t=0 102 20 V * vc(t) 1/10 F 10H Figure 8.6
( xy 7. CHALLENGE: fxy(x, y) = 0< < 2, 0 <y <1 otherwise 0 Find P(X+Y < 1) HINT: consider the region of the XY plane where the inequality is true.
4. Let f(x, y, z) = rytan'() + z sin(xy), < = wy=v²v, z = ". Find fu and , using the chain rule.
Let X and Y have join density
6 f(x, y) =-(x + y)2, 0 < x < 1, 0 < y < 1
Find Var(2X-Y)
Two random variables X and Y are i.i.d. and their common p.d.f. is given by f )- c(1+r) if 0 <r < 1. otherwise. f(3) = 10
Let X. Y be two random variables with joint density fx.x(x,y) = 2(x + y), 0<x<y<1 = 0, OTHERWISE a) Find the density of Z = X-Y b) Find the conditional density of fXlY (x|y) c)Find E[X|Y (x|y)] d) Calculate Cov(X, Z)
Evaluate // e-(x+vº)dA where D = {(x,y): x2 + y2 <1,1 20, y 2 0}.
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
(2) The circuit is at steady state for t<0. Find v(t) for t>0. Answer t=0 ZF Navt)14 T