- #1
HyperbolicMan
- 14
- 0
Question: What is the probability that a random variable X with domain all real numbers will take a value in the closed interval [a,b]?
It seems to me that in order to answer this question you have to know how the real numbers are distributed. Given the appropriate distribution function, you can integrate it from a to b to find the probability.
Common sense says that the real numbers should have a constant distribution (e.g. P(x)=c for all x). However, the integral of any constant function from -[tex]\infty[/tex] to [tex]\infty[/tex] is not 1.
So how exactly are the real numbers distributed?
It seems to me that in order to answer this question you have to know how the real numbers are distributed. Given the appropriate distribution function, you can integrate it from a to b to find the probability.
Common sense says that the real numbers should have a constant distribution (e.g. P(x)=c for all x). However, the integral of any constant function from -[tex]\infty[/tex] to [tex]\infty[/tex] is not 1.
So how exactly are the real numbers distributed?