# Probability and Statistics:?

Polonium. 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?

### 1 Answer

- DixonLv 72 months agoFavourite answer
The Poisson Distribution formula only needs λ, which you have, and you can plug in any Y to get the probability of Y. So just make a table of probabilities from Y = 0 to around y = 10 (or when small enough) and you can answer all parts. Just note that (d) is kind of a trick in that by definition the answer is λ, so don't try to calculate it.

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