4. (Extra-credit 0.5 pt) For what three-point and free-throw percentages would it be advisable to foul a player shooting a three-point shot? Justify your answer.

and this one needs R code ->

3. (4 pts) Neurons, the main information carrying unit of the central nervous system, typically fire action potentials (or "spikes") at low rates spontaneously. If the average spontaneous firing rate of such a cell is 0.2/sec:

a. (1 pt) What type of discrete probability distribution can these data be expected to follow? State the parameter(s) of the distribution and give its formula. What is the expected value and variance of the random variable associated with this distribution? Compute the following probabilities:

b. (1 pt) That the neuron won't fire any spikes in a 10-second period.

c. (1 pt) That the neuron will fire at least one spike in a 10-second period.

d. (1 pt) That the neuron will fire at least two spikes in a 10-second period.