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For a Maxwellian distribution, ⓝd's-G,T)" exp(- the units of f are (v2 + V, + V:))d%,...
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2...
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2 = {[a, b, c, d]T ER+ : a+c= 0,b+d=1}, V3 = {[a,b,c,d)' e R+ : ac =0}. Decide if V1, V2, V3 are subspaces of R4. Explain. Bonus (5pt). If one of V1, V2, V3 is a subspace find a basis for it and find its dimension.
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) f...
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) ....
1.) In lecture, we developed the Maxwell-Boltzmann distribution given as: P(v)dv = 47 (2,16)"exp(-mv7/2kyn) v?dv Explicitly...
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...
. Let W and V be independent random variables where W has a normal distribution with...
. Let W and V be independent random variables where W has a normal distribution with mean equal to Q and variance equal to , and V has açhi-square distribution with r degrees of freedom. V7 then what is the distribution of T A. t-distribution with r degrees of freedom B. t-distribution withr1 degtees of freedom C. F-distribution with 1 and r degrees of freedom D. F-distribution with r and 1 degrees of freedom E. F-distribution with r and r...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem...
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...
Question 3. With regard to the equation: t = tp/(1 – v2/c2)1/2 what does the result...
Question 3. With regard to the equation: t = tp/(1 – v2/c2)1/2 what does the result if v = c or v > c mean? a. nothing b. the speed of light in vacuum is a cosmic speed limit c. time travel to the distant future is possible d. undefined
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question:...
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,)...
[16 marks] Provide concise answers and brief justification and reasoning (a) Determine the period of the function f(t)...
[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)...
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) =...
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...
Problem 3 (10pt). Consider the sets V1 = {[a, b, c, d]T E R*: a+c=0}, V2 = {[a, b, c, d]T ER+ : a+c= 0,b+d=1}, V3 = {[a,b,c,d)' e R+ : ac =0}. Decide if V1, V2, V3 are subspaces of R4. Explain. Bonus (5pt). If one of V1, V2, V3 is a subspace find a basis for it and find its dimension.
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) ....
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...
. Let W and V be independent random variables where W has a normal distribution with mean equal to Q and variance equal to , and V has açhi-square distribution with r degrees of freedom. V7 then what is the distribution of T A. t-distribution with r degrees of freedom B. t-distribution withr1 degtees of freedom C. F-distribution with 1 and r degrees of freedom D. F-distribution with r and 1 degrees of freedom E. F-distribution with r and r...
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...
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,)...
[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...
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