If the calculation is based on equation (33), it should be noted that 



p (k) = p (ra) = - 

 12 



f or 1 < k < 6 and 1 < m < 6 . 



p^(k) = p^(m) = 



for k > 6 and m > 6 . 



p^(k) = p^(m) = 



for k < 1 and m < 1 



The corresponding calculation for P(n) is given in Table 15. 



Table 15. 



Computation of P(n), z = x + y, two unbiased dice. 



n 



Pj(m-n) 



P3(n) 



2 



1/36 



1/36 



3 



(2+l)/36 



3/36 



4 



(3 + 2 + l)/36 



6/36 



5 



(4 + 3 + 2 + l)/36 



10/36 



6 



(5 + 4 + 3 + 2+ l)/36 



15/36 



7 



(6 + 5 + 4+3 + 2+ l)/36 



21/36 



8 



(6 + 6 + 5 + 4 + 3 + 2)/36 



26/36 



9 



(6 + 6 + 6 + 5 + 4 + 3)/36 



30/36 



10 



(6 + 6 + 6 + 6 + 5 + 4)/36 



33/36 



11 



(6 + 6 + 6 + 6 + 6 + 5)/36 



35/36 



12 



(6 + 6 + 6 + 6 + 6 + 6)/36 



36/36 



It is apparent that the cumulative distribution function in Table 15 is the same as that in 

 Table 14. The procedure for calculating p (n), if needed, is obvious. 



b. Second Problem. Myers (1970) discusses techniques which may be used to estimate 

 the probability density function for large storm-generated contributions to the water level 

 on the open beach, and presents probability distribution functions for Atlantic City. He 

 considers three classes of storms: (a) landfaUing hurricanes which come inland near enough 



82 



