Some questions about random variables probability

AI Thread Summary
The discussion revolves around a user seeking help with questions related to random variables and probability before an upcoming quiz. The user initially struggles with one question but finds a solution for the second. Forum members emphasize the importance of showing work and reasoning to facilitate better assistance. A hint is provided regarding the definition of probability over an interval for a bivariate function. Ultimately, the user reports finding the solution through friends, indicating a resolution to their inquiry.
yousif1429
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I have some questions I could not find answer I hope here to get the correct answer

my questions here in this picture ( attached ) 2 questions
 

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Hey yousif1429 and welcome to the forums.

It would help us if you showed your working out and also told us what you are thinking and why you are thinking that.

We can't just solve things for you on these forums per the forum rules, so to help the readers we need to know some of these details.
 
ok i found solutions for second question but the first one i did not found yet
the purpose of these questions because tomorrow i have quiz and my teacher bring this question in last semester and i said for my self may he will repeat it again
please if you know solve the first one please because i looked in my book similar to this question and i did not find i get tired now and my exam is tomorrow i hope some one help me .

thank you ,
 
yousif1429 said:
ok i found solutions for second question but the first one i did not found yet
the purpose of these questions because tomorrow i have quiz and my teacher bring this question in last semester and i said for my self may he will repeat it again
please if you know solve the first one please because i looked in my book similar to this question and i did not find i get tired now and my exam is tomorrow i hope some one help me .

thank you ,

Hint for the number 1: What is the definition of the probability over an interval for a bivariate function? What are the limits for this integral given the information in the question?
 
ok no thank you i found the solution from my friends
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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