Probability function with specification for different ranges ?

[RufusDawes]

The function fx(x) is defined differently for the range 0 to 1 as for values greater than one to 2.
Past x = 2, the function is zero.


When you are asked to find the expected value or variable how are the multiple ranges is all treated ?

Do you need to add both functions together and calculate the expected value using the two functions ?

Does the zero mean that the function has converged ? Do all of these probability like equations need to converge to be valid ?

 

[Stephen Tashi]

When you are asked to find the expected value or variable how are the multiple ranges is all treated ?

Are you saying that you don't know how to do an integration of a function f(x) whose definition involves two different formulae, depending on the range of the variable?

Do you need to add both functions together and calculate the expected value using the two functions ?

Yes, you might need to do two integrals and add the integrals together to get the total integral.

Does the zero mean that the function has converged ? Do all of these probability like equations need to converge to be valid ?

You're just tossing around words without considering whether they mean anything. What do you mean by "the function has converged"? There isn't any question of convergence unless the function is defined as a limit of some sort, where the concept of "convergence" is relevant.

If a function f(x) is defined by two different formulas on two overlapping intervals, then the formulae must produce the same values on the values on any value of x where the intervals overlap. Is that what you're asking?