Marginalization of multiple random variables

**borracho** · July 9th 2009, 07:47 AM

Can someone enlighten me how to marginalize so that I get p(x5) from p(x1, x2, x3, x4, x5)? When summing over x2, x3, x4, and x5 to marginalize, I'm not sure how to write out the conditional probabilities from the joint probability to get down to p(x5).

Thanks!

**Moo** · July 9th 2009, 07:58 AM

Hello,

For example :

You want $\rho_{(x_1,x_2,x_3,x_4)}(a_1,a_2,a_3,a_4)=\mathbb{ P}(x_1=a_1,x_2=a_2,x_3=a_3,x_4=a_4)$

Intersect the set $\{x_1=a_1,x_2=a_2,x_3=a_3,x_4=a_4\}$ by the partition of the universe : $\bigcup_{i\in\mathbb{N}} \{x_5=b_i\}$

So, after some set operations, we get
$\rho_{(x_1,x_2,x_3,x_4)}(a_1,a_2,a_3,a_4)$ $=\sum_{i\in\mathbb{N}} \mathbb{P}(x_1=a_1,x_2=a_2,x_3=a_3,x_4=a_4 \mid x_5=b_i)\mathbb{P}(x_5=b_i)$

Does this help ?

Thread: Marginalization of multiple random variables

LinkBack

Thread Tools

Display

Marginalization of multiple random variables

Similar Math Help Forum Discussions

random variables separable into 2 functions integrated over the same variables

Multiple Random Variables

What's the difference between discrete random variables and continous random variable

Joint PMFs of Multiple Random Variables - Urgent Help

Convergence with multiple variables

Search Tags