Consider a renewal process with hazard function H (t) = lambda theta (t - tau_abs). Here tau_abs > is the absolute refractory period and theta (x) is the Heaviside function. Calculate: the inter-spike interval probability density function rho (tau). Show that the interspike interval coefficient of variance is CV = Squareroot (tau^2) - (tau)^2/(tau) = 1/1 + lambda tau_abs. Write a MATLAB code to simulate the renewal process with Hazard function H (t) = lambda (1 - e^-(t - tau_abs)/tau_rel) theta (t - tau_abs). Here tau_rel > 0 is a relative refractory period. Let lambda = 30Hz. Numerically estimate rho (tau) for (tau_abs, tau_rel) = (3 ms, 1 ms) and (3 ms, 10ms). Numerically estimate the CV as a function of tau_rel over (0, 20ms) with tau_abs = 3ms. Numerically estimate the CV as a function of tau_abs over (0, 20ms) with tau_rel = 3ms. Consider a renewal process with hazard function H (t) = lambda theta (t - tau_abs). Here tau_abs > is the absolute refractory period and theta (x) is the Heaviside function. Calculate: the inter-spike interval probability density function rho (tau). Show that the interspike interval coefficient of variance is CV = Squareroot (tau^2) - (tau)^2/(tau) = 1/1 + lambda tau_abs. Write a MATLAB code to simulate the renewal process with Hazard function H (t) = lambda (1 - e^-(t - tau_abs)/tau_rel) theta (t - tau_abs). Here tau_rel > 0 is a relative refractory period. Let lambda = 30Hz. Numerically estimate rho (tau) for (tau_abs, tau_rel) = (3 ms, 1 ms) and (3 ms, 10ms). Numerically estimate the CV as a function of tau_rel over (0, 20ms) with tau_abs = 3ms. Numerically estimate the CV as a function of tau_abs over (0, 20ms) with tau_rel = 3ms