By G. Barrie Wetherill (auth.)

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**Example text**

Given number, L r Pr(X <; r) = Pr(X = i). 3. , is zero to the left of the range, and for discrete distributions it rises discontinuously to unity on the right of the range. 6. 5 1. Calculate some of the terms of the binomial distribution for the following sets of parameters n (J 5 0·2 10 0·1 50 0·02 100 0·01 Compare these distributions with some of the early terms of the Poisson distribution for p. = 1. PROBABILITY AND PROBABILITY DISTRIBUTIONS 63 2. 2 with the Poisson distribution by the following procedure.

However, if the number of items in the batch is large compared with the number drawn, 50, this dependence of the probabilities can be ignored. Thus if there are, say, 5% of defective items in the batch, the system behaves as a system in which there are 50 independent trials, with a probability of 0·05 of a defective at each trial. This leads to a binomial distribution for the number of defectives, with n = 50, () = 0'05, Pr(r defectives) = 500r(0·05)"(0·95)50-, for r = 0, 1, ... , 50. 05)2 = 0·54 1·2 which is the probability that the number of defectives is two or less.

In studying a certain fatal disease, the following observations were obtained, where y is the logarithm of months to death, Xl is an objective measure of blood properties, and X 2 is the doctor's subjective prognosis, ranked on a five-point scale (1 good; 5 very bad). y 0·51 0·42 0·48 0·39 0·51 0·79 0·58 1·10 0·59 Xl Xs Y Xl x2 2·0 3 4 5 4 4 3 3 4 4 0·72 1·21 1-12 0·76 0·77 1·31 1·02 1·21 1·32 2·9 2·9 3·0 3·1 3·1 3·2 3·3 3·5 3·6 5 3 2 3 2 2 2 2 1 2-l 2·3 2·3 2·5 2·6 2·8 2·8 2·9 Plot a scatter diagram of the data, representing the three variables.