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# CDF - Which definition? watch

1. The book I'm using defines the CDF, F as:

F = P(U<V) where U is the random variable being mapped onto the sample space, V.

Yet online, and in fact in most sources, the CDF is defined as:

F = P(U≤V).

When we want to find the probability of an interval in the given sample space, say P(C), the two give slightly different answers:

P(C) = P(U<V2) - P(U<V1) = P(V1 ≤ U < V2)
or
P(C) = P(U<V2) - P(U<V1) = P(V1 < U ≤ V2)

I don't understand how two slightly different definitions can supposedly give the same answer. Can anyone expand on this and explain if they are the same or they aren't and also why?
2. (Original post by djpailo)
The book I'm using defines the CDF, F as:

F = P(U<V) where U is the random variable being mapped onto the sample space, V.

Yet online, and in fact in most sources, the CDF is defined as:

F = P(U≤V).
The less-than-or-equals definition is the standard one. A typo in your textbook?
3. (Original post by Gregorius)
The less-than-or-equals definition is the standard one. A typo in your textbook?
Can't be a typo because it is used throughout the book
4. (Original post by djpailo)
Can't be a typo because it is used throughout the book
A quick look around finds wikipedia saying that the convention is "not universally used" and that there are problems with the alternative (in the use of discrete distributions, for example). It identifies the Hungarian mathematical literature as using .

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