Computer problem
1
Simulate a coin toss
process consisting in 500 tosses per trial over 10000 trials. Assume P(head=0.01). Compute the mean and variance of this process
and plot on the same graph the sample distribution and a Poisson distribution
with the same mean.
Exercise
You are given the following
data: BABAEAACDDABABAAADAEBABBAABADAAC
1-Estimate the
frequency of each letter and compute the entropy of this estimated
distribution. What is the optimal uniquely decodable binary code given these
data?
You are told that the
data were actually generated according to the following distribution: P(A) = 0.5, P(B)=0.25, P(C)=0.125, P(D)=0.0625, P(E)=0.0625.
2- What would be the
actual optimal uniquely decodable code? What is the optimal code length? How
does it compare to the entropy of P?
3-Compute
the average code length for the code in question 1 given the true distribution.
4-Compute the KL distance between the estimated and true distribution and compare to the difference between the code lengths when using the estimated vs true distribution
Computer problem
2 (optional, no deadline)
Simulate a random
walk model of spiking. Compute the mean, variance, Fano factor, interspike interval distribution and CV. The details of the
model can be found in: