Prove that aX+bY is a random variable for all a,b in R

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Marees

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Given [FONT=MathJax_Math]X and [FONT=MathJax_Math]Y[/FONT] as random variable, how to prove that [FONT=MathJax_Math]a[/FONT][FONT=MathJax_Math]X[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]b[/FONT][FONT=MathJax_Math]Y[/FONT] as random variable for all [FONT=MathJax_Math]a[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]b[/FONT] in [FONT=MathJax_AMS]R[/FONT]?[/FONT](Hint from Karr)​
[FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math]X[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]Y[/FONT][FONT=MathJax_Main]<[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]}[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Size2]⋃[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]∈[/FONT][FONT=MathJax_AMS]Q[/FONT][FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math]X[/FONT][FONT=MathJax_Main]<[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]}[/FONT][FONT=MathJax_Main]∩[/FONT][FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math]Y[/FONT][FONT=MathJax_Main]<[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]}[/FONT]​
How do you interpret this hint? :confused:
 
Marees said:
Given [FONT=MathJax_Math]X and [FONT=MathJax_Math]Y[/FONT] as random variable, how to prove that [FONT=MathJax_Math]a[/FONT][FONT=MathJax_Math]X[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]b[/FONT][FONT=MathJax_Math]Y[/FONT] as random variable for all [FONT=MathJax_Math]a[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math]b[/FONT] in [FONT=MathJax_AMS]R[/FONT]?[/FONT](Hint from Karr)​
[FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math]X[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]Y[/FONT][FONT=MathJax_Main]<[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]}[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Size2]⋃[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]∈[/FONT][FONT=MathJax_AMS]Q[/FONT][FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math]X[/FONT][FONT=MathJax_Main]<[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]}[/FONT][FONT=MathJax_Main]∩[/FONT][FONT=MathJax_Main]{[/FONT][FONT=MathJax_Math]Y[/FONT][FONT=MathJax_Main]<[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math]r[/FONT][FONT=MathJax_Main]}[/FONT]​
How do you interpret this hint? :confused:
Click to expand...

What is your interpretation?

Can you read set-theoretic statements?

Duplicate Post:

http://math.stackexchange.com/questions/171080/

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
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Ok. Is this connected with math.stackexchange? I was trying if people can help me out, too.
 
Let's see if I can explain this:

1) Volunteers are a good thing. They actually make the world a better place.
2) Volunteers aren't necessarily all that sensitive, but if you waste their time, they might stop volunteering.
3) If you post questions in multiple locations, you may receive multiple identical answers.
4) If you receive multiplek identical answers, all but one of those volunteers has potentially wasted their time.
5) If you post in multiple locations to get a faster answer, you are saying your time is more important than volunteers' time. This is in error.
6) If you need instant answers, you should consider paying for them.
7) If you don't show your work or provide any sort of useful feedback, volunteers often feel their time is being wasted.
8) If you want someone to do your homework for you, you should find a friend and trade cooking or house cleaning or something.

So, what say you of this problem you have posted?
 
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