Week 2 - Random Systems

Work out the first three cumulants C1, C2, and C3.

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(b) Evaluate the first three cumulants for a Gaussian distribution

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(a) If ~y(~x) = (y1(x1, x2), y2(x1, x2)) is a coordinate transformation, what is the area of a differential element dx1 dx2 after it is mapped into the ~y plane? Recall that the area of a parallelogram is equal to the length of its base times its heig

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If p(x1, x2) is uniform, what is p(y1, y2)?

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(a) For an order 4 maximal LFSR write down the bit sequence.

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(b) If an LFSR has a clock rate of 1 GHz, how long must the register be for the time between repeats to be the age of the universe (∼ 1010 years)?

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Important Notes

Entropy is the relationship between how surprised you are and the probability of the outcome - are you more surprised the less likely something is to happen but happens? What ifyou're more surprised if something unlikely happens to two independent random variables as you are if something unlikely h appened to only one of them? This is the intuition behind entropy.

Stocahstic processes is a fancy title meaning random vairables where time is one of the variables.

Here are the written notes

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