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 statistics? Explain your answer
To determine if the synapse obeys Poisson statistics, we need to compare the observed failure rate with the expected failure rate calculated using Poisson distribution.
Poisson statistics describe the probability distribution of the number of events occurring in a fixed interval of time or space when events occur independently with a known average rate. In this case, the events refer to synaptic failures.
To calculate the expected failure rate using Poisson distribution, we use the formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where:
- P(X = k) is the probability of getting exactly k events
- e represents the base of the natural logarithm (~2.71828)
- λ is the average rate of events (λ = average number of failures per trial)
First, we need to calculate the average number of failures per trial using the given information. In 1000 trials, there were 300 failures. Therefore, the average number of failures per trial is 300/1000 = 0.3.
Now, let's evaluate if the synapse follows Poisson statistics by comparing the observed failure rate with the expected failure rate.
Expected failure rate using Poisson distribution:
P(X = 0) = (e^(-0.3) * 0.3^0) / 0! = e^(-0.3) ≈ 0.7408
To determine if the synapse obeys Poisson statistics, we compare the observed failure rate (0.3) with the expected failure rate (0.7408). If the observed failure rate is approximately equal to the expected failure rate calculated using Poisson distribution, then the synapse follows Poisson statistics.
Please note that this analysis assumes that each trial is independent and that the average failure rate remains constant throughout the experiment.