1. ## Normal Distribution problem

Suppose X and Y are independent random variables with standard Normal Distributions. The probability of X < -1 is some p (from 0,1) . What is the probability of the event:
X^2 > 1 and Y^3 < -1 ?

a. 3p
b. p^2
c. 2p^2
d. 3p^2

2. Originally Posted by champrock
Suppose X and Y are independent random variables with standard Normal Distributions. The probability of X < -1 is some p (from 0,1) . What is the probability of the event:
X^2 > 1 and Y^3 < -1 ?

a. 3p
b. p^2
c. 2p^2
d. 3p^2
$\Pr(X^2 > 1) = \Pr(X < -1) + \Pr(X > 1) = 2p$.

$\Pr(Y^3 < -1) = \Pr(Y < -1) = p$.

And if $X$ and $Y$ are independent then $X^2$ and $Y^3$ are independent.