Thread: 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!

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.

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

Thanks!

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

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

A probability P measures the 'quantity' of such that the event is realised : . 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

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