[R] Combinations and joint probabilities

[Amelia Livington]

 
Dear R helpers
 
Suppose I have two sets of ranges (interest rates) as 
 
Range 1 : (7 – 7.50, 7.50 – 8.50, 8.50 – 10.00) with respective 
probabilities 0.42, 0.22 and 0.36.
 
 
Range II : (11-12, 12-14, 14-21) with respective probabilities 0.14, 0.56 and 
0.30 respectively.
 
 
My problem is to form the combinations of these ranges in a decreasing order of 
joint probabilities. It is assumed that these ranges are independent.
 
Suppose A represents (7-7.50), B represents (7.50-8.50) and C represents (8.50 
– 10.00).
Also let X be (11-12), Y is (12-14) and Z is (14-21).
                        
These two groups are independent i.e. Prob(A and Y) = P(A) * P(Y)
 
So there are 9 combinations possible as (AX, AY, AZ, BX, BY, BZ, CX, CY and CZ) 
respectively with the joint probabilities (0.059, 0.235, 0.126, 0.031, 0.123, 
0.066, 0.05, 0.202, 0.108) respectively.
 
My problem is
(i)                               How to obtain 
these 9 combinations of probabilities in the sense how do I obtain the various 
combinations of these two ranges along-with their respective probabilities; 
(ii)                             How to arrange 
these 9 probabilities in descending order against the respective group 
combination i.e. for the combination AY, the joint probability is maximum at 
0.235, followed by CY at 0.202 and so on.
 
I sincerely apologize as perhaps I might not have raised the query properly. I 
have become member of this group today only and its been hardly a week since I 
have started learning R language. I have easily done this in Excel. My output 
should be something like this – 
 
Combination   Probability
AY                   0.235
CY                   0.202 
AZ                  0.126
BY                   0.123
CZ                  0.108
BZ                  0.066
AX                  0.059
CX                  0.050
BX                   0.031
 
 
I request you to guide me.
 
Thanking in advance
 
Amelia
 
 
 


      
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