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1. ### Error Propagation

I see. Thank you very much HallsofIvy. This was bugging me for a long time.
2. ### Error Propagation

Recently I came across an example for working out error propagation, and I'm having trouble following the steps: A = 100 \pm 1% B = 10 \pm 1% AB = (100 \pm 1%).(10 \pm 1%) = \left\{1000 \pm \left[\left(100.1\%\right) \pm \left(10.1\%\right)\right]\right\} // get confused here, how does...
3. ### PDF (probability density function)

Yes, it is a triangle distribution! Bloody hell! Thank you so much for guiding me through this problem Vela. I am really really thankful for your tutoring :D
4. ### PDF (probability density function)

Thank you. This is what I get for the integration: \int_{\frac{2-a}{3}}^1} 1-x dx = \left[x - \frac{x^2}{2}\right]_{\frac{2-a}{3}}^1} = \frac{a^2 +2a + 1}{18} \int_{\frac{2-a}{3}}^0} 1+x dx = \left[x + \frac{x^2}{2}\right]_{\frac{2-a}{3}}^1} = \frac{-a^2 +10a - 16}{18} And for the...
5. ### PDF (probability density function)

Just when I was feeling some relief, I have to integrate a triangle function... \int_{\frac{2-a}{3}}^\infty p_X(x) dx = \int_{\frac{2-a}{3}}^\infty \Lambda(x) dx = \int_{\frac{2-a}{3}}^\infty 1 - x dx So then I end up with... \left[x - x^2/2\right]_{\frac{2-a}{3}}^\infty And then I...
6. ### PDF (probability density function)

-3X+2\le a X\ge (2-a)/3
7. ### PDF (probability density function)

I understand what you're saying but having functions inside brackets and trying to diffrentiate triangle functions is making me go crazy. I keep on backtracking... I have something like this: F_Y(y) = P(Y\le y) = -3\Lambda(X) + 2 So then I diffrentiate with respect to y or x? And what...
8. ### PDF (probability density function)

I'm sorry I still do not understand what to do. My lecturer was not very thorough when he explained random signals and processes. From my limited understanding: p(x)dx = \Lambda(X)dx = (1-\left|x\right|)dx = -1 I'm sorry I just do not understand. I do not like to give up this easily but...
9. ### PDF (probability density function)

Hi everyone, I have a simple question (assuming since it was only worth 5% of total marks in the exam) about the PDF of a random variable. Given that PDF of random signal equals p(X) = \Lambda(X), where \Lambda is the triangle function, what would be the PDF of the random signal Y, Y = -3X...
10. ### Voltage drop across diode

So if the anode side was less positive (e.g. +3V) than the cathode side (e.g. +5V), the diode would not conduct? I took the above diode from the AND gate circuit below. I cannot figure out how this circuit works. I'm going to run through what I understand of it, and if somebody can please...
11. ### Voltage drop across diode

Hi guys, I have a very simple question but which is messing with my mind. I'm trying to figure out the voltage drop across a diode when it is reverse biased, and I'm just not getting anywhere. Can someone please take a look at the attached image and explain to me what the voltage drop across...

Any ideas?
13. ### Fourier Transforms

Performing the intergral with integration by parts 3 times, I get the following: F(t3) = 4 / \omega4 With the full transformation F(t3) = 2/pi * \int_{0}^\infty 4.ei.\omega.t / \omega4 Which also equals F(t3) = 8/pi * \int_{0}^\infty cos\omega + j.sin\omega / \omega4 Now using...
14. ### Fourier Transforms

I just want to confirm if I'm following the right approach. Step 1: I need to find the sine and cosine transforms of f(t) = t3 when 0 ≤ t < ∞? Step 2: I then need to rearrange to somehow get the equaton in the picture?
15. ### Fourier Transforms

After reading the notes, this is how far I got: f(t) = 2/pi. I(0 - inf)fcomega.cosomega.td.omega However, when I start evaluating the fcomega integral, I have the limits 0 - infinity and I'm left with [t3.cosomega.t / omega] between 0 and infinity. I can't seem to progress from this stage...
16. ### Half-Range Fourier Series

Ok here is what I gather so far: I am looking for the sine half-series, which is bn.Sin(nt) from the Fourier series. So, bn = I{t.sin(t).sin(nt)} between 0 and 2pi ... which goes to ... bn = I{t.sint(1+n)} between 0 and 2pi? Is that correct? EDIT: ... which gives me 0. I think I...
17. ### Help with inverse Laplace transforms

Part 3: It should be A/(s+1) + (Bs + c)/(s2 + 1) Hence 2 = A.(s2 + 1) + (Bs +c).(s + 1) You can then find all the values using s = -1, 0 and 1.
18. ### Half-Range Fourier Series

Homework Statement Question: Find the half-range Fourier sine series for the function f(t) = t sin(t) Problem: According to all the examples I have gone through, they all have a limit when asking for the half-range. However, my teacher, in the question posted above, has not specified any...
19. ### Fourier Transforms

Homework Statement The problem is related to Fourier transforms. Since my teacher only cared to spend 2 lectures explaining the whole of this topic, I just cannot get my head around some of the principles involved. The question is as follows: Use the Fourier Transform formulas with the...
20. ### Fourier Series - Convergence

Homework Statement Please see attached image. From the given information, I am having trouble deriving the left and right hand limits, I just can't figure out what these are... http://img176.imageshack.us/img176/9334/fstih3.png [Broken] Homework Equations None needed. The Attempt...
21. ### Double Integration - Finding the limits

Ok that is much more clear now. Thank you.
22. ### Laplace from first principles

I see. That makes sense. Thank you very much for your help.
23. ### Double Integration - Finding the limits

Homework Statement Find the limits of the integral of z = f(x,y) over the region bounded by the x-axis, and the semi-circle x2 + y2 = 4, y ≥ 0 Homework Equations The Attempt at a Solution Where do I start on this question? I can't understand what it is asking. IbaIdc Am I...
24. ### Laplace from first principles

Homework Statement Find, from first principles, the Laplace transform of f(t) = sin2(3t) Homework Equations sin23t = 1/2(1-cost(6t)) L{SINat} = a/(s2 + a2) The Attempt at a Solution I already have the solution. s/2(s2 + 36) What I want to ask is what does the first principles part...