In testing synaptic transmission, you found that there were 300 failures in 1000 trails of stimulating a presynaptic neuron. The average EPSP size was .7 mV +/- .2mV (mean +/- SD), and the average 'mini' EPSP size was .6mV +/- .1mV. Does the synapse obey Poisson stati...
To determine if the synapse obeys Poisson statistics, we need to compare the observed failure rate to the predicted failure rate based on Poisson statistics.
The failure rate in this case is the number of failures divided by the total number of trials. In your experiment, there were 300 failures in 1000 trials, so the failure rate would be 300/1000 = 0.3.
In Poisson statistics, the failure rate is determined by the mean. The mean is given by the equation: mean = e^(-lambda), where lambda is the average number of failures. If the synapse obeys Poisson statistics, then the observed failure rate should be equal to the predicted failure rate based on the mean.
To calculate the predicted failure rate, we need to find the mean lambda. Since the failure rate is 0.3, we can solve for lambda using the equation: 0.3 = e^(-lambda).
Taking the natural logarithm (ln) of both sides of the equation, we get: ln(0.3) = -lambda.
Now, we can calculate the predicted failure rate by taking the exponential of -lambda: predicted failure rate = e^(-ln(0.3)).
To determine if the synapse obeys Poisson statistics, compare the observed failure rate (0.3) to the predicted failure rate. If they are close in value, then the synapse is likely to obey Poisson statistics.