0
$\begingroup$

If i have K independent Random Variable:

$X_1,X_2,x_3,\cdot\cdot\cdot\cdot\cdot\cdot\cdot\cdot\cdot, X_k$ What would be the CDF of the sum of their Joint Distribution? $f_{X_1+X_2+X_3+...+X_k} (z)$ z<=1.

I cant figure out what would be their respective density functions and integration limits.

$\endgroup$
1
$\begingroup$

By independence:$$F_{X_1,\dots,X_k}(x_1,\dots,x_k)=P(X_1\leq x_1,\dots,X_k\leq x_k)=$$$$P(X_1\leq x_1)\times\cdots\times P(X_k\leq x_k)=F_{X_1}(x_1)\times\cdots\times F_{X_k}(x_k)$$

$\endgroup$
1
$\begingroup$

If they are independent, then

$$Pr(X_1 \le x_1, \ldots, X_k \le x_k ) = \prod_{i=1}^k Pr(X_i \le x_i)$$

That is the joint CDF is just the product of individual CDF.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.