INCESSANT TRANSMISSION 9/2 



Head, then the probability of its going to state 5 is ^ ; and so would 

 be its probability of staying at 4. 



All other transitions have zero probability. So the matrix can be 

 constructed, cell by cell. 



This is the matrix of transition probabilities. (The reader should 

 be warned that the transposed form, with rows and columns inter- 

 changed, is more common in the literature ; but the form given has 

 substantial advantages, e.g. Ex. 12/8/4, besides being uniform with 

 the notations used throughout this book.) 



We should, at this point, be perfectly clear as to what we mean by 

 "probability". (See also S.7/4.) Not only must we be clear about 

 the meaning, but the meaning must itself be stated in the form of a 

 practical, operational test. (Subjective feelings of "degree of 

 confidence" are here unusable.) Thus if two observers differ about 

 whether something has a "constant probability", by what test can 

 they resolve this difference ? 



Probabilities are frequencies. "A 'probable' event is a frequent 

 event." (Fisher.) Rain is "probable" at Manchester because it is 

 frequent at Manchester, and ten Reds in succession at a roulette 

 wheel is "improbable" because it is infrequent. (The wise reader 

 will hold tight to this definition, refusing to be drawn into such 

 merely speculative questions as to what numerical value shall be 

 given to the "probability" of life on Mars, for which there can be 

 no frequency.) What was said in S.7/4 is relevant here, for the 

 concept of probability is, in its practical aspects, meaningful only 

 over some set in which the various events or possibiHties occur with 

 their characteristic frequencies. 



The test for a constant probabihty thus becomes a test for a 

 constant frequency. The tester allows the process to continue for a 

 time until some frequency for the event has declared itself. Thus, 

 if he wished to see whether Manchester had a constant, i.e. unvarying, 

 probability of rain (in suitably defined conditions), he would record 

 the rains until he had formed a first estimate of the frequency. 

 He would then start again, collect new records, and form a second 



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