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 statis...
To determine whether the synapse obeys Poisson statistics, we need to compare the observed number of failures to the expected number of failures based on a Poisson distribution.
The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate of occurrence. In this case, the events are failures in synaptic transmission.
The average rate of occurrence of failures can be calculated by dividing the number of failures (300) by the total number of trials (1000):
Average rate of failures = (Number of failures) / (Total number of trials)
= 300 / 1000
= 0.3
Now, we can use the Poisson distribution to calculate the expected number of failures for a given average rate of occurrence. The Poisson probability mass function is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where:
- X is the random variable representing the number of failures
- k is the number of failures
- λ is the average rate of failures
To apply this formula, we need to calculate the probability of observing 0, 1, 2, 3, ..., up to the maximum number of failures in our dataset.
Using the average rate of failures (0.3), we can calculate the expected number of failures for each value of k. Then, we can compare the observed and expected number of failures to assess whether the synapse follows Poisson statistics.
Please note that the information provided in your question is not sufficient to perform this calculation. We need the maximum number of failures observed during the trials to calculate the Poisson probabilities accurately.