Question

If \(X\) and \(Y\) are 2 independent random variables, will functions of these random variables also be independent?

For example, if I have a function \(f(k)=z^k\), then would \(f(X)=z^X\) and \(f(Y)=z^Y\) be also independent?

Answer 1

I feel like this should be true.. but would it happen for every type of function?

Answer 2

I think so, it's independent. To my discrete prof, that z doesn't relate to anything else, but the function it is in. He said that: "Think of 'Mom' and 'Dad', this guy calls his parents are 'Mom' and 'Dad', that girl calls her parents are 'Mom' and 'Dad', too. But those 'Mom' and 'Dad' are independent."

Answer 3

or what if 3^x and 3^lnx and 3^(1/x) or 3^(-x) they work independently, right?

Answer 4

Would that be the "same" x in all those functions o.O?

Answer 5

I don't think so, they are different. x is just the name of variable, if I don't use it, I can use t, u, v, and so on. It doesn't represent for anything else but itself in its function.

Answer 6

I can give you examples: y = x^2 +3 , the value of x in this function give you value of y which graph is a parabola
y = x +3 , although we still have x =0, x =1, x =2 as we have in the previous one, but the value of y is on the line, which doesn't relate to y in the previous one.
Is it clear?

Answer 7

so, x in parabola relate to its y only.

Answer 8

If they were independent, would there not be any overlap?

Answer 9

they can!! definitely they can in some conditions.

Answer 10

in some interval, they "meet" to each other, but not all

Answer 11

for example above, x =0, both y = x^2 +3 and y = x+3 have the same value y =3

Answer 12

but just happenly they meet,

Answer 13

oh is it that they cannot overlap over some interval, but can at points? Oh dear this has been awhile :S I'm so sorry