1. ## random variable

the random variable U has the normal distribution with mu=0 and variance=2 and V=U^2

Calculate P(V \geq 1)

confused!

2. Hello,

Originally Posted by skystar
the random variable U has the normal distribution with mu=0 and variance=2 and V=U^2

Calculate P(V \geq 1)

confused!
$P(V \ge 1)=P(U^2 \ge 1)=P(|U| \ge 1)=P(U<-1)+P(U>1)$

Does this help ?

3. hmmm not really

4. Originally Posted by skystar
hmmm not really
Then, you use the normal distribution, by transforming it into a standard normal distribution (Normal distribution - Wikipedia, the free encyclopedia). Everything is in the link...

5. arh i see how did you know to go from $U^{2}$ to |U|?

6. Originally Posted by skystar
arh i see how did you know to go from $U^{2}$ to |U|?
I took the square root

$a=b^2 \implies b=\pm \sqrt{a} \Longleftrightarrow |b|=\sqrt{a}$

This is quite the same here ^^

Edit : I'm sorry, I misread the question... Well, we know the law for U, not for UČ. And from one to another, there is only the step mentioned above

7. Originally Posted by skystar
the random variable U has the normal distribution with mu=0 and variance=2 and V=U^2

Calculate P(V \geq 1)

confused!
The more interesting question is to find the pdf for V (you'll find it done a couple of times in different contexts on these boards). Then you can check the answer you got using Moo's excellent help .