. Let_x(t,0) = X¸sin(2Ãt+0) where the phase angle O is a random variable. The PDF of 0 is sketched below Compute μ = E(x(t,0)) f(0) 1/π TU 2π

Q: Find the dy/dx of the following: 2x +3 1) y = logs 4x - 3 2) y = x?Inx 3) y = esin4x 4) y = 4*(2*)…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let X1, ... , Xn be a random sample have the pdf 1 (1-0) f(x,0) = -(x),0 < x < 1, 0<0 < ∞. Find mle…

A: The likelihood of X1,X2,...,Xn is given as: L=∏i=1nfxi,θ=∏i=1n1θxi1-θθ=1θ∏i=1nxi1-θθ…

Q: find the a general solution to dy/dt = {{-9,12},{6,-8}}y

A: (.)  Given ,            (.)  Consider a system of differential equation ,…

Q: Q14) (A) (t) sin(2t) e-st dt = (B)e- e- (C) se-F. s2+4 (D) 2e-8. 82 +4 (E) e

A: The integralFrom the shifting property, we haveHere

Q: (i) B(2,3)-

A:

Q: 15) Let f(x) = f In (t² – 5)dt. Find f'(x) and then also find f"(x).

A:

Q: If the RHS (Right Hand Side-the source) function of a second-order differen tial equation with a…

A: Here we have to go option wise and choose the option with; y(0) = y'(0) = 0. Clearly we can see…

Q: An LTI system has impulse response h(t) = (1/t“) u(t – 1). Show that the system is BIB0 stable if a…

A:

Q: ctan x (2) Let h(x) = t dt, calculate h'(T/3). ww. t2 + 2

A: Solve the following

Q: An atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise…

A: From the given information, ψx=14*2π14e-x2-4x+41024ψx2=142π14e-x2-4x+410242…

Q: Let F(x) = Vt2 + 19 dt. Find 6. (a) F(9) = (b) F'(9) =| (c) F"(9)

A: Topic = Derivative

Q: Exercise 1.3.8: Find an implicit solution for dy dx = x² + 1 -, for y(0) = 1. y² + 1'

A:

Q: дх 5 + 2¹(1² 1 -)dt

A: To find the derivative

Q: Let y = 3x2 + 3x + 4. If Δz = 0.1 at x = 5, use linear approximation to estimate Ay Δy ~

A: we have given

Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x) b) Let y=cosx-sin.x , show that…

A:

Q: Draw the bifurcation diagram for dy/dt = y(a-y)

A: We can use concept of critical points in order to solve the given problem.

Q: Calculate dy/dt using the given information. x^4/3+y^4/3=2; dx/dt=6, x=1, y=1

A:

Q: Let 7(t) = Find '(t) F (t) =

A:

Q: 1. Let the random variable Y have pdf as f(y\A) = e®=e=t(e-1), y>0,1>0. Show that W = e – 1] ~ x²…

A:

Q: Example 11: 3 If F(x) = J Int dt, find F'(xr) 2+sin 2.x

A: To determine the F'(x).

Q: a. B(6,5)

A:

Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

A:

Q: Suppose f(x) = [ 6t² /1+t° dt .

A:

Q: 4. a) Find the general solutions of the following differential equations. Express the general…

A:

Q: 8. Consider the following model for the populations of two species in competition in a given…

A:

Q: Ex. 130. Given the s-domain signal: F(s) ( 7 s^2 + Determine the steady state value of f(t) using…

A: we have Fs=7s2+3s+9s3+10s2+13s limt→∞ft=lims→0sFs

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: e'dy + (5t + ye')dt = 0.

A:

Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: Find the solution of the wave equation when initial velocity equal to O and initial deflection is…

A:

Q: Given f(x)=4x3, 0<=x<=1 Find moment generating function of X

A: The moment generating function of any function, f(x) is calculated asMXt=∫-∞∞e-txfxdx

Q: 2022 Use appropriate techniques to solve dx dt 1 xe2t+x

A: Given: dxdt=1xe2t+x To find: Solve this differential equation using appropriate method. Integration…