Let's say that you're recording from a neuron with equipment that breaks down from time to time. If you don't see a spike recorded by the equipment, you want to know whether to attribute that to the equipment being broken or to the neuron really not spiking The following directed graph describes this scenario: E R where E indicates whether the neural recording equipment is working (E = 1) or broken (E = 0), N indicates whether the neuron spiked (N = 1) or did not spike (N = 0), and R indicates whether a spike was recorded (1 =1) or not recorded (R =0) by the equipment. The neuron spikes independently of whether the recording equipment is working or broken, with prior probabilities: P(E = 1) = 0.9 P(N - 1) - 0.25 Given the values of E and N, a spike is recorded with the following probabilites: P(R = 1E = 1, N =1) =1 P(R = 1|E = 1, N =0) =0 P(R = 1|E = 0, N = 1) =0.1 P(R = 1|E = 0, N =0) =0.1 (a) What is the prior probability that the neuron did not spike? (b) What is the probability that the neuron did not spike, given that no spike was recorded? Why does this answer make sense intuitively compared to the answer in part (a) (i.c., which is larger)? (c) What is the probability that the neuron did not spike, given that no spike was recorded and that the equipment was broken? Why does this answer make sense intuitively compared to the answer in part (b) (i.c., which is larger)