0
$\begingroup$

Let random variable X has dual normal distribution with mean vector $\mu$ and

covariance matrix $\sum$

$$X= \left ( \begin{array}{ccc} x_1 \\ x_2 \end{array} \right )$$ $$\mu= \left ( \begin{array}{ccc} 3\\ 5\end{array} \right )$$ $$\sum= \left ( \begin{array}{ccc} 4 & -2\\ -2 &4 \end{array} \right )$$ Let $y = 2x_1 - 3x_2$ Find $P(y>4)$

I know how to find $P((x_1, x_2) \subset D )$, but i have no idea how to find $P(y>4)$

$\endgroup$
1
$\begingroup$

hint

condition on one of the variables: $$ \mathbb{P}[y>4] = \int_{-\infty}^\infty \mathbb{P}[y > 4|x_1=t] f_{x_1}(t) dt... $$

$\endgroup$

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.