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4. (34 points) A neuron spikes according to a homogeneous Poisson process with rate A. (a) (2 points) What is the mean ISI of this

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4. (34 points) A neuron spikes according to a homogeneous Poisson process with rate A. (a) (2 points) What is the mean ISI of this neuron? (b) (4 points) What is the probability that a given ISI is greater than the mean IST? (c) (7 points) What is the expected ISI given that it is larger than the mean ISI? Hint: You may find it useful to calculate Pr(T = tT > 1/x) with Bayes' theorem, and subsequently calculate the (conditional) expectation: ETT > 1/X] t Pr(T = tT > 1/X)dt

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