In the 1910 article The Probability Variations in the Distribution of Particles (Philosophical Magazine, Series 6,

In the 1910 article "The Probability Variations in the Distribution of α Particles" (Philosophical Magazine, Series 6, No. 20, pp. 698-707), E. Rutherford and H. Geiger described the results of experiments with polonium. The experiments indicate that the number of α (alpha) particles that reach a small screen during an 8-minute interval has a Poisson distribution with parameter λ = 3.87. Determine the probability that, during an 8-minute interval, the number, Y, of α particles that reach the screen is
a. Exactly four.
b. At most one.
c. Between two and five, inclusive.
d. Construct a table of probabilities for the random variable Y. Compute the probabilities until they are zero to three decimal places.
e. Draw a histogram of the probabilities in part (d).
f. On average, how many alpha particles reach the screen during an 8-minute interval?