WP 34S binomial bug?

[BarryMead]

The cumulative distributions calculate the probability that the random variable is ≤ a given value (Norml, Binom, Poiss etc.). The upper variants calculate the probability that the random value is ≥ the given value (Norml_u, Binom_u, Poiss_u etc.). The suffix u was chosen since the result mathematically is the upper tail integral of the probability function.

If the distribution is continuous (i.e. it can have real values like 3.7 or –1.638) the lower integral is bounded by –infinity and x, and the upper integral is bounded by x and +infinity. Both sum up to 1, so e.g. Norml_u(x) = 1 – Norml(x).

If the distribution is discrete it can take only integer values: a random experiment may have three or four successes, but not 3.74. Here the lower CDF (Binom, Poiss etc.) is the sum of the probabilities for 0, 1, 2, .... x successes, while the upper CDF (Binom_u, Poiss_u etc.) is the sum for x, x+1, x+2, ... n successes. The probabilty for exactly x successes occurs in both cases, so the upper and lower probabilities do not sum up to 1. However Binom(x) + Binom_u(x+1) = 1. The Binom, Poiss (Poissλ), and Geom distributions operate on discrete random variables, while the rest operate on continuous random values. Throughout Appendix I, the distribution plots show dots along the curve for the discrete distributions and smooth lines for the continuous distributions.


If the paragraph above (or something similar) were included in Appendix I of the manual as part of the explanation of the first (Binom) distribution, that would completely answer all of the questions I had about the probability distribution functions. Thank you ever so much Dieter, Pauli ,Walter and lrdheat for constantly improving the WP-34s and its documentation.