In connexion with a certain experiment an instrument was devised which, in each consecutive time period of th of a second, either gave an impulse or did not give an impulse. It was hoped that the probability, p, of the impulse occurring would be the same for every time period and independent of when the previous impulses occurred.

To test the instrument it was switched on and a note was made of the number of periods between the start of the test and the first impulse and thereafter of the number of periods between consecutive impulses. The test was continued until 208 impulses had been noted and the data were then grouped into the number of impulses which occurred in the first period after the previous one, the number in the 2nd period after the previous one (i.e. after one blank period) and so on. These grouped data are given in the table. Period after Period after previous previous impulse No. of impulse No. of (or start) impulses (or start) impulses 1st 81 7th 2nd 44 8th 43 4 3 3rd 24 9th 5 4th 22 10th wi 3 5th 13 6th 9 Total 208 Fit the appropriate probability distribution, based on the above assump- tions, to these data and test for goodness of fit. The makers of the instrument claim that the probability of an impulse occurring during any period is 0-35. Test whether the data are consistent with this claim. (Lond. B.Sc.)