Problem 1. We model the number of times a neuron fires with a Poisson process. Suppose that on average the neuron fires A > 0 times per second. We start at time t = 0 seconds. (a) Given that the neuron fires exactly 3 times in the first 2 seconds, find the conditional probability that the first arrival happened after 0.5 seconds. (b) What is the probability that the second firing happens after 4 seconds? (c) Given that the first firing happened in within 1 second, what is the con- ditional probability that the second firing also happened within 1 second