I Distribution function and random variable

AI Thread Summary
The discussion centers on understanding how the value of F_X(x) is derived in Table 2.1, specifically for x=1 where F_X(x)=1/2. A participant clarifies that the calculation involves counting the number of elements in the sample space, which totals four elements out of eight. This results in the probability of 4/8, simplifying to 1/2. The explanation highlights the importance of accurately interpreting distribution functions and random variables. Overall, the conversation emphasizes the foundational concepts of probability calculations in statistics.
PainterGuy
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Hi,

I cannot figure out how they got Table 2.1. For example, how come when x=1, F_X(x)=1/2? Could you please help me with it?

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You count four elements there in the table, OK ? So it is 4/8=1/2.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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