I 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 'How do E[X] and E[|X|] relate?'

Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...
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