9/19 ANSWERS TO THE EXERCISES 



9/19. 1: (i) [ 4 () 7 <") 1 2 1 5 



2: Only if the combinations of « and /? are restricted to some three of 

 the four possible. 



9/20. 1 : A distortion, for a second inversion will restore the original without 

 loss. 2: A distortion if each tension evokes a distinct frequency. 

 3: A corruption, for various tensions evoke the same (zero) output. 



9/21. 1 : /fi is log29. H2 is found from: 



Symbol received: 123456789 

 ProbabiUty: I I I i i i i i 



and is 2-948 ; so the equivocation is 0-222 bits per symbol. 2: Equivo- 

 cation = 0; yes, the new messages are transmitted unambiguously. 

 4: 0-00299. 5: The table of events and probabilities is : 



(The probabilities are most simply found by dividing 20,000 cells first 

 into 19,000 and 1,000; and then dividing these into cells mis-diagnosed 

 and the rest; finally divide by 20,000.) Hi =0-365 bits/cell; Hi = 

 0-324 bits/cell. So equivocation = 041 bits/cell. 



10/4. 1: The cat acting on, perhaps playing with, a dead mouse. 2: If such 

 were possible, it would correspond to the cat doing something that brings 

 a dead mouse back to life! 3: C is lethal to M if not one of C(Mi), 

 . . . , C{M^) is in Ml, ... , M^. 



10/5. (i) Temperature and humidity ; (ii) the oxygen in the climber's blood and 

 all that depends on it; (iii) the directions of the light rays passing through; 

 (iv) the illumination of the objects that would otherwise be invisible 

 after sunset; (v) the temperature of the food and, consequently, the 

 degree of its bacterial contamination; (vi) the intensity of illumination 

 of the plant's leaves; (vii) the intensity of illumination of the retina; 

 (viii) the pressure (at high intensities) on the sole; (ix) the contact- 

 pressure, which is kept at zero; (x) the distance between shell and target, 

 which is kept zero or small. 



11/3. l:X^n^ 1: D being given, R should take the value that satisfies 



' ' y p a 



37 = R-2D; so R should take the value 37 + 2D. 3: The main 

 diagonal (S.2/10) has the outcomes "skid corrected", the other two 

 cells the outcomes "skid exaggerated". 4: Zero— they will all be c's, 

 whatever the variety in D's selections. 5: Yes. 



11/4. l:Yes. 



2- X ^ 2 ^ "^ ^ . 



' ^ ^ ^ or 8 a a a or 8 



3: R simply plays y on all occasions, without reference to D's move. 



4: Yes, and he should use the transformation 



Mr. A Mrs. B Mr. C 



^ Sherry Gin Sherry 



284 



