Undergrad Distribution function and random variable

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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.
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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