Messages passed amongst neurons in the brain can be recorded using an external electrode, and they...

 

Transcribed Image Text:

Messages passed amongst neurons in the brain can be recorded using an external electrode, and they show up as a series of spikes of equal magnitude. These spikes can be modelled by a Poisson random variable with rate 6000 spikes per minute. The PMF of the Poisson RV is given by: P(N = k) for k= 0, 1, 2, ... (a) What is the probability of recording no spikes in the first 100 milliseconds? (b) What is the probability of recording between 5 to 10 spikes (both included) in the [300ms, 400ms] time range? ake-a k! = (1) Leave your answers as an expression in terms of a sum of 1 or more exponentials. Hint: The parameter a of the Poisson RV is the average number of event occurrences in a specified time interval, so utilize the given information to find out this parameter. Messages passed amongst neurons in the brain can be recorded using an external electrode, and they show up as a series of spikes of equal magnitude. These spikes can be modelled by a Poisson random variable with rate 6000 spikes per minute. The PMF of the Poisson RV is given by: P(N = k) for k= 0, 1, 2, ... (a) What is the probability of recording no spikes in the first 100 milliseconds? (b) What is the probability of recording between 5 to 10 spikes (both included) in the [300ms, 400ms] time range? ake-a k! = (1) Leave your answers as an expression in terms of a sum of 1 or more exponentials. Hint: The parameter a of the Poisson RV is the average number of event occurrences in a specified time interval, so utilize the given information to find out this parameter.

Answer rating: 100% (QA)

ANSWER a The time interval of interest is 100 milliseconds which is 01 minutes The Poisson rate para... View the full answer