Stochastics: discrete random variables

  • Thread starter sunrah
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  • #1
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Homework Statement


X1 and X2 are two independent discrete random variables with
P(X1 = k) = c3-k
P(X2 = k) = d4-k

for k in natural numbers and where X1, X2 in natural numbers is almost always valid. 0 is not include in N.

Find constants c and d.

Homework Equations




The Attempt at a Solution


Since I'm joining this class late in the semester I don't know where to begin. Any help is appreciated!!
 

Answers and Replies

  • #2
Curious3141
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Hint: what must the total probability of all possible events (in the entire sample space) be?

Another hint: geometric series.
 
  • #3
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Hint: what must the total probability of all possible events (in the entire sample space) be?

Another hint: geometric series.

do you mean sum to infinity?

[itex]\Sigma^{\infty}_{K=1} c3^{-k} = 1[/itex]

I see that the series (sn) = c3-k converges.
 
  • #4
Curious3141
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do you mean sum to infinity?

[itex]\Sigma^{\infty}_{K=1} c3^{-k} = 1[/itex]

I see that the series (sn) = c3-k converges.

So what's the sum?
 
  • #5
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So what's the sum?

ya, so in this case (sn) = 3-k converges against 1/2. So c = 2

thanks!
 
  • #6
Curious3141
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ya, so in this case (sn) = 3-k converges against 1/2. So c = 2

thanks!

I would've simply said [itex](c)(\frac{1}{2}) = 1 \Rightarrow c = 2[/itex]. But, yes, you've got the idea. :smile:
 

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