Stochastics: discrete random variables

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.

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!!

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

Another hint: geometric series.

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?

$\Sigma^{\infty}_{K=1} c3^{-k} = 1$

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

Curious3141
Homework Helper
do you mean sum to infinity?

$\Sigma^{\infty}_{K=1} c3^{-k} = 1$

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

So what's the sum?

So what's the sum?

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

thanks!

Curious3141
Homework Helper
ya, so in this case (sn) = 3-k converges against 1/2. So c = 2

thanks!

I would've simply said $(c)(\frac{1}{2}) = 1 \Rightarrow c = 2$. But, yes, you've got the idea.