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Probability function with specification for different range ?

by RufusDawes
Tags: function, probability, range, specification
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RufusDawes
#1
Mar26-12, 05:39 AM
P: 163
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 ?
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chiro
#2
Mar26-12, 06:00 AM
P: 4,573
Quote Quote by RufusDawes View Post
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
#3
Mar27-12, 03:31 AM
P: 163
Quote Quote by chiro View Post
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
#4
Mar27-12, 04:30 AM
P: 4,573
Probability function with specification for different range ?

Quote Quote by RufusDawes View Post
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?


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