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]

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 ?

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]

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.

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]

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 ?

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?

 

[blue_raver22]

Yes, it is possible to have multiple equations for the probability function depending on the range of x. This is because the probability function can be tailored to fit the specific scenario or data being analyzed. For example, if the range of x is from 0 to 100, the probability function may be defined as f(x) = 1/100. However, if the range of x is from 100 to 200, the probability function may be defined as f(x) = 1/200. In this case, there would be two different equations for the probability function depending on the range of x. The specific equation used would depend on the specific range being analyzed. It is important to carefully define the range and corresponding equations for the probability function in order to accurately calculate probabilities.