If I have one variable that is standard-normal distributed, say X ~ N(0,1) and another variable Y = X^2. What would the mean and variance of Y be?
I tried looking at a graph of x^2 vs. x^4 to try and think about this more intuitively. The result is that the x^4 graph is flatter for longer (i.e. lower gradient for more values of x) but I'm struggling to work out the implications this would have for a normal distribution.