# Math Help - random variable

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 U². 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 .