My question whether there is another way of approaching this problem other than realizing the probability in question can be rewritten as:
The reason that I ask is that I had a hard time seeing it.
My question whether there is another way of approaching this problem other than realizing the probability in question can be rewritten as:
The reason that I ask is that I had a hard time seeing it.
Hey downthesun01.
The transformation you used is probably the best way to do it. Some alternatives include looking at (X-1)^2 [in terms of a chi-square distribution after centering) or using the transformation theorem to get the exact PDF of X^2 + 2X.
Again, the best thing in terms of simplicity is to do what you have done.