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Math/calculus question

S

SurgicalShark

Golden Member
I have following equation of which one term is non-linear (involving F), how can I solve this equation?

Knowns (constants): s1, x1, s2, x2
Unknowns: a1, a2, a3

a1 + a3 = s1 - x1
a2 - a3 = s2 - x2
F(x1+a1+a3) - F(6-x1-a1-a3) = 10

where F is general cumulative probability density function of which value exists, so for example F(2) is known.

I need to find out values of a1, a2 and a3 from these equations. Any help is appreciated.
 
a1 + a3 = s1 - x1
a1 - a3 = s2 - x2

If x1, x2, s1, and s2 are known, you can get a1 and a3 directly from these 2 equations.

 
Originally posted by: Howard
a1 + a3 = s1 - x1
a1 - a3 = s2 - x2

If x1, x2, s1, and s2 are known, you can get a1 and a3 directly from these 2 equations.
Click to expand...


I am sorry there was a typo...it should have been a2 instead of a1. Thank you.
 
I don't think your problem can be solved. The arguments to F in the third equation are both constants, since they are both funcitons of a1+a3 which is a constant (s1-x1). So you'd have 3 unknowns and 2 eq's.
 
Well, arguements in third equation inside bracket are not per se constants because they will be in terms of a1 and a3. I am thinking that third equation involves an integral which is non-linear and hence may not be solvable with given three equations. Is that right?
 
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