Discrete Random Variable

#1
Hey all, I have a Discrete Random Variable taking on values x= 1,3,3^2,3^3,...3^m and f(x)=P(X=x)=c/x for some constant c, find value of c.


How do i do this question im 100% lost
 

Dason

Ambassador to the humans
#4
That's not the only thing that needs to be true.

For example is
f(0) = .5
f(1) = .5
f(2) = .5
f(x) = 0 for any x not equal to 0,1,2

a valid probability distribution?
 

Dason

Ambassador to the humans
#6
What? I already defined f(0), f(1), f(2). You can't just change them. So why isn't that a valid pdf? (Hint: Think about the sum)
 

Dason

Ambassador to the humans
#8
Exactly. So going back to your original problem we can see that you need to find the value of c that makes the sum over all possible values equal 1.
 
#9
I understand now BUT i still dont see how to calculate C if the problem is 3^m, i mean if i had a definitive set i can do it but i dont understand this method..Im thinking C=1 but i dont know if thats correct or not..
 
#14
Hey all, I have a Discrete Random Variable taking on values x= 1,3,3^2,3^3,...3^m and f(x)=P(X=x)=c/x for some constant c, find value of c.


Thats all the question asks
 

BGM

TS Contributor
#15
Of course I know the question. I just want to make sure: do you know which geometric series are you aiming at? Can you write that down?
 

BGM

TS Contributor
#17
So I am still trying to provide hints so that you can apply the method mentioned by Dason at #8 (as you claim you understand that)

Maybe another question: Can you show that the sum of the pmf of a Geometric distribution equals to 1?
 
#18


I understand that all the vals must add up to 1 but when i take the formula i get the following:
s=1((1-3^n)/(1-3))
-2s=1-3^n
S=(1-3^n)/2

where s=c BUT that doesnt give me a value because n is still unknown, i dont know why im having this much trouble with this problem heh.
 

Dason

Ambassador to the humans
#20
Also note that r isn't 3. You're pdf is of the form f(X=x) = c/x so you want to sum 1 + 1/3 + 1/3^2 + ... 1/3^m