In the 1910 article The Probability Variations in the Distribution of Particles (Philosophical Magazine, Series 6, No. 20, pp. 698707), E. Rutherford and H.

• 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 (Use Poisson Distribution Equation) 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?