Chapter 8.2, Problem 4RQ

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Solve this problem and show all of the work

The joint probability density function of two discrete random variables X and Y is given by p(x, y)=c(2x+y), where x and y can assume all integers such that 0≤ x≤2, 0≤ y ≤ 3, and p (x, y)= 0 otherwise. a) Find the value of the constant c. (c) Find P(X≥1, Y≤2). (b) Find P(X=2, Y= 1).

A wattmeter is connected with the positive lead on phase "a" of a three-phase system. The negative lead is connected to phase "b". A separate wattmeter has the positive lead connected to phase "c". The negative lead of this wattmeter is connected also to phase "b". If the input voltage is 208 volts line-to- line, the phase sequence is "abc" and the load is 1200 ohm resistors connected in "Y", what is the expected reading of each of the wattmeters? (Hint: draw a phasor diagram)

1- Write the mesh equation for the circuit below. Solve the equations using Crame method (matrix and determinant), and find the current of resistor 4 ohm. 6 A www 10 Ω w 6Ω www 12 V + 402 www 12 Ω 2- Write the nodal equations for the circuit below. You do not need to solve the equation just write the matrix equation. R3 ww 8Ω R₁ 201 5 A 12 3A R₂40

Please solve these 3 questions in detail

1. Please draw the root locus by hand for the following closed-loop system, where G(s) s+8 S-2 and H(s) = Find the range of K for stability Input R(s) Output C(s) KG(s) H(s) s+6 = S-2

The state-space Jordan Canonical Form of the following system is: Y(s) 8-5 U(s) (+1)(+3) Select one: O a. -1 0 0 A = 0 -1 0 B: ... ... ... 0 0 C [4 1.5 1.5], D=0 b. -3 1 0 0 A = 0 -3 0 1 B ... 0 0 -1 C -4 -1.5 1.5], D=0 ○ C. -3 1 0 A = 0 -3 0 1 ,B= ... 0 0 ○ d. C [4 1.5 1.5], D=0 -3 1 0 0 A = 0 -3 0 1 , B: ... ... 0 0 -1 C [4 1.5 1.5], D=0 -4 1 If= x and (0): = then 2(t) is: -4 0 Select one: a. x2(t)=4te2t O b. x2(t) = e2t+2te2t Oc. 2(t)=-4te-21 Od. 2(t) e2-2te-2 =