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Math Help - What does addition operation on RVs mean?

  1. #1
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    What does addition operation on RVs mean?

    Hello Everyone!

    I've read in a text somewhere what looks like the following:

    X and Y are two RVs. Let Y = aX + b for some two real a and b.

    First of all, what does scalar multiplication of an RV mean?

    Second, what does addition of a constant to an RV mean?


    Any help is appreciated!
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  2. #2
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    Re: What does addition operation on RVs mean?

    Hello,

    Basically, the RV takes some values. Suppose you have X following a Bernoulli distribution (the most simple) with parameter p.
    Then P(X=0)=1-p and P(X=1)=p.
    What is the distribution of Y=aX+b ? Its only possible values will depend on those of X : a*0+b=b and a*1+b=a+b.
    So P(Y=b)=P(a*X+b=b)=P(X=0)=1-p and P(Y=a+b)=p.
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    Re: What does addition operation on RVs mean?

    Alright yeah I was always thinking that an RV, for instance X, is only an abstraction.

    Thanks!
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    Re: What does addition operation on RVs mean?

    The real definition of a rv is that it's a function that goes from \Omega (the set of all events) and \mathbb R for example (it could be \mathbb C as well).

    When one actually write X, it's X(\omega), \omega \in\Omega.
    When you write a*f(x)+b it's the same.

    A probability P measures the 'quantity' of \omega such that the event is realised : P(X=5414775)=P(\omega ~:~ X(\omega)=5414775). Here, the event is {X=5414775}.

    I'm trying to give you a deeper explanation, if you don't understand, don't worry you'll know it in time if you continue studying probability
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  5. #5
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    Re: What does addition operation on RVs mean?

    Well I'm studying about random processes right now

    You know it's always technical around here, very mechanic. I know my way around RVs, integrals, etc. but I only started to learn how they popped up a while after I first got to learn them.

    Thanks again
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