Find value of a and b such that F(x) is a valid cumulative distribution function

[chessmath]

Hi
I have a question , the question asks find value of a and b such that F(x) is a valid cumulative distribution function?

1-a*exp(-x/b) x≥0
F(x)=
a*exp(x/b) x<0

My attempt to solve the problem:

I know F(x) when x goes to ∞ in 1 and when x goes to -∞ is 0. also I know F(x) should be right continuous and it is non-negative. However, non of them help me to find even one of the constants, any help will be appreciated ?

 

[Dick]

Hi
I have a question , the question asks find value of a and b such that F(x) is a valid cumulative distribution function?

1-a*exp(-x/b) x≥0
F(x)=
a*exp(x/b) x<0

My attempt to solve the problem:

I know F(x) when x goes to ∞ in 1 and when x goes to -∞ is 0. also I know F(x) should be right continuous and it is non-negative. However, non of them help me to find even one of the constants, any help will be appreciated ?

If you want it to be continuous at x=0 what are the limits of both forms of F as x->0? Though actually if you only have right continuous, I don't think you have that restriction. Hmm. Not sure. I can see some restrictions on the values of a and b, but not how to calculate them.