Need it asap show work please Let i + 2z B(2) = 4- 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, B(2) < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from -i to e3ri/4 and then bouncing from e3mi/4 to 1. Denote by the curve representing the trajectory of the particle. Without evaluating the...
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6. Let B(2) = i + 2z 4 - 2iz (a) Find the smallest positive real value M such that for every z on the closed unit disk D, |B() < M. [6] (b) A particle on the complex plane is trapped within a wall built along the unit circle. It travels from –i to e3ri/4 and then bouncing from e3vi/4 to 1. Denote by y the curve representing the trajectory of the particle. Without evaluating the integral, show how...
(a) Suppose that i, X2,... , In is an i.i.d. sample from Exp(1). Show that, for a standard normal random variable Z b) Show Г(n) by differencing both sides of the approximation in part a. Then set a -0 to get Stirling's Formula. 5. Suppose that Y is an id sample from Negative Binomial (n,p). Give a normal approximation of Yn use CLT, when n is large. 6. (Mandatory for Graduate Student. Extra credit for undergrad.) Let Ai, converges to...
Solve the system. -3x+y+4z=1 x+y+z=0 -2x+z=-1 x+y-2z=0 Please show all steps! I thought I got the correct answer but my numbers don't work for the last given equation. Thank you!
Data for Parallel Circuit: I (Exp) I (Theo) Diff% V(Exp) V(Theo) Diff% R1=100.1 Ohms 49.97mA 49.95mA ? 4.991V ? ? R2=553.9 Ohms 9.02mA 9.027mA ? 4.991V ? ? Vs= 5V 58.99mA 58.98mA Please respond to the following: 1. Provide mathematical details of your theoretical derivations for the parallel circuit. Show the calculations of currents and voltages that were reported on the table above. 2. How do the theoretical values compare with the experimental values? If there are any differences between...
I need help with 1.b) 1a. Assume the unitary operator U-exp(1?/4lâ??? +â?â01. show that the matrix relation for the beam splitter, is identical with the unitary transformation Hint: use the Baker-Hausdorf lemma on page 13 of Gerry/Knight. 1b. operator U-exp(??/2la??, + âtaol). Obviously, for ?-?/2 the result in 1a is retrieved. Calculate the beam splitter matrix corresponding to the more general unitary
Q2. Consider the plane P C R3 given by the equation 2z-y+2z 7 and the point v2 (a) Show that the point p-5lies in P and calculate the distance between p and v (b) Find the point qE P that lies closest to v (c) What is the distance of v to P? (d) What is the angle between the vectors v - q and p -q? (e) Does the pythagoras theorem apply to the triangle formed by the points...
(1 point) Consider the vector field F(x, y, z) = (2z + 3y)i + (2z + 3x)j + (2y + 2x)k. a) Find a function f such that F = Vf and f(0,0,0) = 0. f(x, y, z) = b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral / F. dr. (1 point) Verify that F = V and evaluate the line integral of F over the given path: F =...
7. Suppose that Xi,..., Xk are independent random variables, and X, ~ Exp(B) for i = 1, . . . , k. Let Y = min(X1 , . . . , Xk). Show that Y ~ Exp(Σ-1 β).