Statistics for Environmental Engineers

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conditions as Table 19.2, can be constructed by differencing the entries in Table 19.2. For example, if p = 0.05, we expect an average of nx = 0.05(20) = 1 success in a 20 trials. In one particular experiment, however, the result might be no successes, or one, or two, or three.

Some examples based on the binomial acute toxicity bioassay will demonstrate how these functions are used. Each test organism is a trial and the event of interest is its death within the specified test period. It is assumed that (1) theoretical probability of death is equal for all organisms subjected to the same treatment and (2) the fate of each organism is independent of the fate of other organisms. If n organisms are exposed to a test condition, the probability of observing any specific number of dead organisms, given a true underlying random probability of death for an individual organism, is computed from the binomial distribution.

From Table 19.2, the probability of getting one or no deaths is Pr(x < 1) = 0.74. From Table 19.3, the probability of observing exactly zero deaths is Pr(x = 0) = 0.36. These two values are used to compute the probability of exactly one death:

Pr(x = 1) = Pr(x < 1) — Pr(x < 0) = 0.74 — 0.36 = 0.38

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