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  1. M

    Marginal probability mass function

    A biased coin lands heads with probability p and tails with probability q. An experiment consists of tossing the coin until a second head appears. Let T1 denote the number of tosses until the first head appears and let T2 denote the number of tosses (counted from the start) until the second...
  2. M

    Magnetic field plane wave

    oh i get it. k = sqrt(3^2 + 4^2) = 5 when i find E in phasor form from the given H, how do i know what direction it should be?
  3. M

    Magnetic field plane wave

    is there a reason you chose the denominator as 5?
  4. M

    Magnetic field plane wave

    The magnetic field expression for an electric field of a plane wave in air in the time domain is H(t) = y3sin(ωt + 3x + 4z). Find the frequency of the wave. i am having trouble where to begin on this problem. i know how to solve if there is only 1 direction variable (i.e. just x or just z)...
  5. M

    Steady state tracking error

    thank you! i thought the degree sign was a 0 this whole time -___-
  6. M

    Steady state tracking error

    I am trying to understand steady state tracking error. I was looking over one of the example problems in my textbook and this is what it said: G(s) = (-1)/(100(s^2-10.791)) D(s) = K(s+5)/(s+10) Td(s) = 1/s as it states above I don't understand how they got the value 3300... I got 2156 when...
  7. M

    Mode of operation for transistor

    i solve for Ie then do the KVL for the CE loop. then solve for Ic from that equation. then get Ib from the relationship Ib = Ie - Ie. if Ib and Ic are both positive then the saturation mode assumption is correct. thanks for pointing me in the right direction!
  8. M

    Mode of operation for transistor

    Vcc = Vbe,on + Vb --> Vb = 2.5 - 0.7 = 1.8 Vb/1000 + (Vb-Vc)/300 = 0 1.8/1000 + 1.8-Vc/300 = 0 --> Vc = 2.34 Ic = 1.8/1000 = 1.8 mA 2.5 = Vec + 300Ic + 1000Ic --> Vec = .16 since Vec = 0.2 in this problem and Vec is less than this, the transistor is not in active mode so i...
  9. M

    Mode of operation for transistor

    what confuses me about this is the position of Vc. normally, it is the voltage across the bottom resistor, but since there are two resistors with a node in between, is Vc the voltage across the 300-ohm resistor? or does Ic occur in both the 300-ohm and 1k-ohm resistor
  10. M

    Mode of operation for transistor

    i'm unsure. is it the voltage at that node between the two resistors?
  11. M

    Mode of operation for transistor

    VBE = VBE,on = 0.7 V (as defined in the text)
  12. M

    Mode of operation for transistor

    I am trying to determine the mode of operation for the following circuit and find the voltages and currents: I am given that β = 50 I know that VEC > VEC,sat for a transistor in active mode I applied KVL on the right loop and got: VCC = 300Ic + 1000Ic + VEC VEC = VCC - 1300Ic i'm...
  13. M

    Centroid of a root locus

    i just want to make sure I'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros) the equation i have is s2 + 2s + 8 / s(s2 + 2s + 10) so the zeros are -1 + i√7 and -1 - i√7 and the poles are 0, -1...
  14. M

    Block diagram simplication

    I am having trouble trying to obtain Y/R from the block diagram below: the only thing i understand so far is that the bottom right loop is a feedback loop and can be simplified to 1/(s+a1). i know b1s can be obtained from the right loop, but i am having trouble getting to that point. i know it...
  15. M

    Simplifying an expression

    I am trying to simply G1 = G1(1+F1) / (1 + G1F2(1+F1)) in terms of G1, G2, H2, and H3 where F1 = G2/(1-G2H2) and F2 = G3 / (1-G3H3) i got the result (G1(1-G2H2)(1-G3H3) + G1G2(1-G3H3)) / ((1-G2H2)(1-G3H3) + G1G3(1-G2H2) + G1G2G3) however, the book gives the result with a +1 in the...
  16. M

    Energy waveform

    Woops, misread your question. I thought you meant it was already on for 30 minutes and then off for the next 30 minutes so the power was like a pulse train. I thought for energy It's a graph that keeps increasing (never dropping) because it is a plot summing total heat energy since time t=0.
  17. M

    Energy waveform

    It would be 50 watt-hour for the hour long time period. then the next hour would be 50 again so total would be 100, etc., etc. if i plotted it over time, it would be a line with positive slope, yes?
  18. M

    Energy waveform

    i'm still confused as to what the graph would look like. is the total energy delivered over one period 500T? ... i think i just understood why T/2 to T is not 0 with that question
  19. M

    Energy waveform

    why additional? what other energy is there? or where does it come from? i only know of energy being equal to ∫p dt = ∫ Ri2(t) dt, and isn't p 0 from T/2 to T?
  20. M

    Energy waveform

    i would assume it just repeats, and from T/2 to T it would be zero and again from 5T/2 to 3T. but would it be somewhat like a sawtooth wave?
  21. M

    Energy waveform

    From the given waveform (of current), sketch the energy from t = 0 to t = 2T. Given: R = 10 Ohms, i = 10 Amps I'm having trouble with this even though it's probably really easy. I know WR = ∫Ri2(t) dt so for one period, for example, I have ∫10(102) dt with limits of integration from 0 to T/2 =...
  22. M

    Voltage across R,L,C

    thanks for the help. i got VR = Im*R = 1 VL = Im*XL = 2√2 VC = Im*XC = 2√2 - 1
  23. M

    Voltage across R,L,C

    Imax = Vmax/Z => Z = 1 (1) Z = sqrt(R2 + (XL - XC)2) cosθ = R/Z, θ = 45° 1/√2 = R/1 R = 1/√2 From (1) I get C = 1/(4-√2) I am not 100% sure this is correct
  24. M

    Voltage across R,L,C

    I am trying to find the effective voltage across each element (R,L,C) of a series RLC circuit like the one below. I am given the following values: Ieff = 1 Amp, Veff = 1 V, i(t) lags v(t) by 45°, L = 1, f = 2/2∏ Hz, L = 1 H What I have done so far: Veff = Vm/√2 => Vm = √2 Ieff = Im/√2 => Im =...
  25. M

    PMF for the sum of random variables

    For a sum of two independent uniform discrete random variables, Z = X + Y, what is the probability mass function of Z? X and Y both take on values between 1 and n I know that for the sum of independent rv's the PMF is a convolution so... Ʃ(1/k)(1/n-k) from k = 1 to n
  26. M

    PMF for the sum of random variables

    For a sum of two independent uniform discrete random variables, Z = X + Y, what is the probability mass function of Z? X and Y both take on values between 1 and L I know that for the sum of independent rv's the PMF is a convolution so... Ʃ(1/k)(1/n-k) from k = 1 to L but I'm wondering...
  27. M

    PMF of a random varible

    so it would be e-λm - e-λ(m+1) which can be written as e-λm(1-e-λ) .. would this be binomial or geometric?
  28. M

    PMF of a random varible

    for a random variable X with parameter λ, Y = m if m < X < m + 1 what is pmf of Y? it's basically asking for P[m< X < m+1] i know how to solve this for P[m < X < m + 1] ... it would be e-λm - e-λ(m+1) because P[a < X < b] = Fx(b) - Fx(a) and i know the PDF of an exponential random variable...
  29. M

    Y and z 2-port parameters

    yep, thanks. i just had a few algebraic errors that threw me off.
  30. M

    Y and z 2-port parameters

    are my Y parameters correct? just wondering because i don't want to be trying to use them to check if my Z parameters are correct if they aren't right in the first place..
  31. M

    Y and z 2-port parameters

    when using Ib - Ic = 2v1 I got v1 = Ia - Ib = Ia- Ic - 2v1 = Ia + (1/3)Id - 2v1 ====> v1/I1 = 1/3 and v1/I2 = 1/9 plugging in values to find the remaining parameters i got v2/I2 = 1/2 and v2/I1 = 0 so for Z parameters i got Z = [1/3 1/9; 0 1/2] The inverse of this is [3...
  32. M

    Y and z 2-port parameters

    I am solving for the Y and Z parameters for the circuit below: For Y, I used the following equations by applying current sources at the terminals va is the node at the 2v1 dependent source (va-v1)/0.5 + (va-v2)/1 = -2v1 I1 = v1/1 + (v1-va)/0.5 I2 = v2/0.5 + (v2-va)/1 I got Y = [3 -2/3; 0 8/3]...
  33. M

    Nodal analysis

    ultimately, i will be solving for y-param. i was able to do so using mesh analysis instead, but i was hoping to try and obtain the nodal equations to double check my answers.
  34. M

    Electric field in a hollow cylinder

    but why not Rin to Rout?
  35. M

    Nodal analysis

    the dependent sources are throwing me off. are the equations at least partially correct?
  36. M

    Electric field in a hollow cylinder

    since in the example in the document it asks for Rin < r < Rout.. why does it integrate from Rout to r??
  37. M

    Nodal analysis

    For the following circuit, can someone please correct my equations for nodal analysis (KCL) I am especially unsure about my second equation because of the dependent voltage source to the left of the node. 1) I1 = (V1 - 3I2)/1 2) 0 = V3/2 + (V3 -V2)/2 3) I2 = (V2-V3)/2 + 2V3
  38. M

    Electric field in a hollow cylinder

    An infinitely long thick hollow cylinder has inner radius Rin and outer radius Rout. It has a non-uniform volume charge density, ρ(r) = ρ0r/Rout where r is the distance from the cylinder axis. What is the electric field magnitude as a function of r, for Rin < r < Rout? for this problem, when...
  39. M

    Thevenin equivalent

    so is it because when you short the voltage source the elements in parallel are shut off, too?
  40. M

    Thevenin equivalent

    it's a current source
  41. M

    2 port network Y parameters

    thanks for that. i just realized now you had said Va = 0 according to the way i had defined it. that cleared things up.
  42. M

    2 port network Y parameters

    i obtained the correct answer by transforming the dependent current source into a voltage source in series with the 2 ohm resistor. i was doing something wrong in the node method. I'm still not sure what it is.
  43. M

    2 port network Y parameters

    Va is the node voltage between the two 2-Ohm resistors. why is the first equation incorrect?
  44. M

    Thevenin equivalent

    For the circuit below, can someone please help me understand why Zeq = 0 (in words...not by solving): I know Vth = 50<0° since this is the voltage drop across the parallel elements. I don't understand why the equivalent impedance would be 0. I know when you shut off a voltage source...
  45. M

    2 port network Y parameters

    for the following circuit, i am trying to find the y parameters i have found y11, y12, and y22 to match the answer that my text provides, but i am having trouble with y21 the solution given is y11 = 1.5, y12 = -0.5, y21 = 4, y22 = -0.5 in trying to solve for y21, i get 4.5 this is...
  46. M

    Q function (gaussian random variable)

    For X ~ N(μ, σ), what is P[|X-μ] < σ] in terms of the Q function? I know that P[|X-μ] < σ] can be decomposed into P[X > -σ + μ] + P[X < σ + μ] I'm not sure what to do next. i know P[X < σ + μ] can be expressed as 1 - phi(σ + μ - μ / σ) = Q(1), but I'm not sure how to approach P[X > -σ + μ]. I...
  47. M

    Uniform random variable

    Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M
  48. M

    Cumulative distribution function

    is z the entire area of the square since it can take on any value from 0 to b in both the x and y directions?
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