00:01
For part a to calculate the probability that the neuron fires more than three spikes in 50 milliseconds we can use the poisson distribution formula which equals p of x which is greater than k which equals 1 minus p times x which is less than or equal to k.
00:24
So given the firing rate of a neuron a is 20 hz we can convert it to spikes in 50 milliseconds by multiplying by the duration.
00:42
So the firing rate in 50 milliseconds equals 20 spikes per second times 50 divided by 1000 which equals one spike.
01:02
Now we need to calculate the probability of firing more than three spikes in which k is greater than three using the poisson distribution p of x is greater than three equals one minus p of x which is less than or equal to three.
01:24
Now using the poisson distribution formula we can calculate the probabilities for x is less than or equal to three.
01:34
So for p of which x equals zero that is e to the power of negative one times one to the power of zero divided by zero which equals 0 .3679.
01:57
For p of x equals one we have e to the power of negative one times one to the power of one divided by one and this equals 0 .3679.
02:13
For p of x equals two we have e to the power of negative one times one to the power of two divided by two which equals 0 .1839.
02:28
For p of x equals three we have e to the negative first times one to the third divided by three which equals 0 .0613.
02:42
So now adding up all the numbers we can say that p of x which is less than or equal to three which equals p of x equals zero plus p of x which equals one plus p of x equals two plus p of x equals three which equals 0 .3679 plus 0 .3679 plus 0 .1839 plus 0 .0613 which equals 0 .9809.
03:23
Finally the probability that the neuron fires more than three spikes in 50 milliseconds is p of x is greater than three which equals one minus p of x which is less than or equal to three which equals one minus 0 .9809 which equals 0 .0191...
