Elementary Statistical Methods by G. Barrie Wetherill (auth.)

By G. Barrie Wetherill (auth.)

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By G. Barrie Wetherill (auth.)

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They can never occur together) then Pr(A or B) = Pr(A) + Pr(B). 6). We also see that the law cannot be used as it stands with events which can occur together. 7), + 2: Pr(exactly r seeds germinate) r=80 = Pr(A or 0) + Pr(A & 0). 89 r seeds germinate) r=75 The following diagram represents the position. The probabilities of events A, 0, A or 0, and A & 0 are obtained by adding together the probabilities of the outcomes indicated. Possible outcomes. 1 The addition law of probabilitie8 The reader will see that whenever any events A and B have outcomes in common, these outcomes are counted twice by the right.

The table shows very clearly that there is a relationship between the two variables. The frequency distribution along each column - for daughters having fathers in a given height group - clearly depends on the height of the father. 0 0 0 Another method of plotting continuous data in two variables is to use a scatter diagram, and this is illustrated in the following example. 7. Anderson and Cox (1950) investigated the relationship between the strength and diameter of wool fibres. The breaking load per unit crosssection, and the diameter, were measured for 185 fibre pieces 1·5 cm long.

3. Calculate the distribution of the number of digits between zeros in a series of truly random digits. Obtain a table of random digits and gather some empirical data for comparison. 4. f. of the geometric distribution. + 5. *Suppose that the probability that an event occurs in the interval (t, t <5t) is A <5t, and denote by P Q:(t) the probability that there have been x events up to time t. Show that PQ:(t + bt) = PQ:(t)(l - A bt) and Po(t + bt) = Po(t)(l - A bt). Hence show that PQ:(t) = e-At +PQ:-1A bt, x = 1,2, ...

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