Probability function with specification for different range ?

RufusDawes

I understand a probability function can be defined according to range ?

So for example,

0>x f(x) = 0

for 0>x>100 f(x) = 1/100

to work out probability it is integration of that function.

So how does it work if for some other range there is a DIFFERENT functions ?

Is it that there will be multiple equations for probability depending on x ?

chiro

Hey RufusDawes.

You do the same thing, but break the integral up into pieces for each appropriate interval.

For expectation, variance etc: same thing: split up the integral according to the intervals and do the integration to get mean, variance, etc.

RufusDawes

So what do I do when the upper limit of the range approaches a discrete value (a whole number) on both ranges.

If there are 2 functions one with a limit 0>x>1 and 1>=x>2 and the other is for x>=2 the integrals of the whole thing should = 1 ?

does that mean that I can use the value of 1 as the upper bit for the first integral as it is so small it won't affect the area ?

chiro

You treat function 1 in range 1 and function 2 in range 2. As long the PDF is a valid probability density function, then it's ok to do this. Are the functions for 0 > x > 1 and 1 >= x > 2 analytic? In other words can you for each range describe a continuous analytic function?