For a Maxwellian distribution, ⓝd's-G,T)" exp(- the units of f are (v2 + V, + V:))d%,...
1.) In lecture, we developed the Maxwell-Boltzmann distribution given as: P(v)dv = 47 (2,16)"exp(-mv7/2kyn) v?dv Explicitly derive the following: a.) Show that this distribution is normalized. b.) For helium atoms at 500 K, use the error function in order to calculate the fraction of particles traveling in the range of 1500 m/s to 2000 m/s. c.) Produce an expression for <Vavy. (Note: Not the root square average as presented in lecture.) d.) Transform this distribution into a distribution in energy...
Consider the differential equation: d y 6y--6 exp-2). d t 6.1 (1 mark) Find a solution of the form y(t) - Cp exp(-2t) for this differential equation, and enter the value of Cp below. You have not attempted this yet 6.2 (1 mark Any solution yh of d yh d t is of the form C exp(r t) for an appropriate value of r. What r? Remark. The general solution of the differential equation labelled (1) above is y(t) ....
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
[16 marks] Provide concise answers and brief justification and reasoning (a) Determine the period of the function f(t) = n+|cos(t)(3+)sin(3tt) (b) Consider the 4-periodic function g(t) that is defined as g(t)=-(x-1)2+1 for te (0,2. Does an approximation of this function by a Fourier series converge faster for the odd or the even extension. (c) Consider the function h(t) cos2(t)+sin2 (t). Are the coefficients by of the Fourier series of this function equal to 0 for all n? (d) Consider the...
Figure 13-1 13) Find the voltage across the capacitor in Figure 13-1. A) 0.633 V B) -4.9 V C) 5.37 V D) 10.7 V 14) If the resistance increases in Figure 13-1, the impedance ________. A) decreases B) increases C) remains the same D) becomes zero 15) As the frequency approaches the resonant frequency in Figure 13-1, the voltage across the resistor ________. A) becomes increasingly unstable B) increases C) remains the same D) decreases Figure 13-2 16) If the...
Y(z) c(t), C(s) r(t), R(S) + - et), E(S) E*(s), Ez To- D(z) G (s) = (1-e-STºys H(s) 32. If the system above has Y(z)R(z)= 1+z), and if the input is the unit step r(t)=u(t), then the signal y[n]= u[n]-e-Tou[n-1) | u[n]+u[n-1] a) c) u[n] + u[n-1) d) none above 33. If the system above has Y(z)/R(z)= 1+z), the dc gain of the system is C(z)/R(z)= b) 1/2 c)2 d) none above a) o 34. If the system above has...
In the circuit below, vy(t)=20coswt V, v2(t) =30cos(wt-90°) Vand w=1000 rad/s. By applying Mesh Analysis, formulate two equations of the form; aly+b/2 = c; dly+el2 =f(a, b, c, d, e and f should be in rectangular form). Then solve for the mesh currents 14 and 12 give your answer in polar form) 15 mH 200 F V 10 3
A particle slides along a straight wire so that a--k/v where a is the acceleration, v is the velocity and k-20 m3/s. The particle stars at X 0, t-0, with a speed vo 10 m/s. 2. When the particle is at x = 4 m, the speed v is most nearly A. 2.49 m/s B. 3.46 m/s C. 5.29 m/s D. 6.93 m/s E. 7.50 m/s F. 8.62 m/s G. 8.88 m/s H. 9.13 m/s I 9.81 m/s J. 10.00...
(a) Determine R, R,, and R Assume gr1 (b) Determinei,,i,ふi4.is, is, and i,' alf in terms oft,. (Hini; Use the current-divider rule at the drain of Q,) (c) Determine v, t, and u, all in terms of v, (d) If บุ is a 5-mV peak sine wave and RJ,-20, sketch and clearly label the waveforms of v, U, and t, D 7.68 Design the double-cascode current source shown in Fig. P7.68 to provide 0.2 mA and the largest possible sig-...