Some questions about random variables probability

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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 'Two interesting number theory tricks'

First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...
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