Question

ExpoNeuron has designed a neural stimulator drug that engages dopamine receptors with a interaction times that follow the exponential distribution with a mean off-rate of 100 Hz. UniNeuron has come up with a rival stimulator drug whose interaction times can be modeled using the uniform distribution spanning [2 ms, 18 ms]. To activate a neuron, approximately ?05 drug molecules are delivered per receptor. Assume that drug molecules interact serially with their target receptor and a drug molecule is degraded immediately after dissociating from a receptor.

(a) Lab testing indicates that total interaction time must exceed one second for a receptor to be successfully activated. As a statistically-literate clinician, which of the two stimulators would you recommend and why?

(b) New lab results indicate that interactions lasting longer than ?.? seconds are unsafe. Given this new evidence, does your answer to the above question change?

(c) It turns out that both ExpoNeuron and UniNeuron successfully launch their neural stimulators in the market. Net annual returns fromExpoNeuron’s stocks are estimated to be normally distributed with a mean of ?0% and a standard deviation of ?%. Likewise, returns from UniNeuron’s stocks are also normally distributed with a mean of ? % and a standard deviation of ?%? What is the probability that in a certain year UniNeuron performs better than ExpoNeuron?

Answer 1