1. ## Discrete Random Variable

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

2. ## Re: Discrete Random Variable

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

3. ## Re: Discrete Random Variable

f(x)>=0 in order to be true.

4. ## Re: Discrete Random Variable

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?

5. ## Re: Discrete Random Variable

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

6. ## Re: Discrete Random Variable

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)

7. ## Re: Discrete Random Variable

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

8. ## Re: Discrete Random Variable

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. ## Re: Discrete Random Variable

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..

10. ## Re: Discrete Random Variable

You might want to recall the Geometric series

11. ## Re: Discrete Random Variable

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

Any one ?

13. ## Re: Discrete Random Variable

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

14. ## Re: Discrete Random Variable

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.

15. ## Re: Discrete Random Variable

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?