# Discrete Random Variable

#### ITman95

##### New Member
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

What needs to be true about f(x) for it to be a valid probability distribution?

#### Dason

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?

#### ITman95

##### New Member
I would say no because f(0)= 0, f(1)=.5 f(2)=1 right ? I dont think im understanding you correctly.

#### Dason

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)

#### ITman95

##### New Member
I see, its because the values do not add up to 1 right ? (.5+.5+.5+=1.5)

#### Dason

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.

#### ITman95

##### New Member
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..

#### ITman95

##### New Member

in this case a=1, r=3 but i dont know what s and n are?

#### BGM

##### TS Contributor
Which series you want to calculate? Maybe write out some terms can help you to figure out the problem.

#### ITman95

##### New Member
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.

#### BGM

##### TS Contributor
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?

#### ITman95

##### New Member
Any ideas guys, this homework assignment is due tonight and need to submit it soon

#### BGM

##### TS Contributor
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?

#### ITman95

##### New Member

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.