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HW4 (Due 11/1)
Consider a parallel color Gaussian channel with 4 “sub-channels” of noise powers \(\sigma_1^2=1\), \(\sigma_2^2=2\), \(\sigma_3^2=4\), \(\sigma_4^2=5\).
Find the capacity when the total signal power is \(20\)
Find the capacity when the total signal power is \(5\)
Consider an unbiased dice and say we throw the dice 10 times (\(N=10\)). Use the bounds and equations described in class
Please upper bound the total number of types
Please upper and lower bound the total number of sequences for type \((0.1,0.2,0.3,0.4,0,0)\)
Please upper and lower bound the probability of getting a sequence of type \((0.1,0.2,0.3,0.4,0,0)\)
Let say a fair dice is thrown 10,000 times and the average of the squares of all outcomes is larger than 20. How many ones do you expect?
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