suppose $X$ and $Y$ are independent random variables with standard normal distributions. The probability of $X<-1$ is some p which lies in the open interval (0,1). what is the probability of the event: $X^2 > 1$ and $Y^3 > 1$.
I have started with $P(X<-1)= P(X>1) = p$ (i think its right) But now stuck at how to proceed from here... I'm thinking of using cdf but not able to fit it in?