I have a exercise, which I don't know how to show. It goes like, X is a continuous random variable with support $(-\infty,\infty)$. Consider the random variable $Y=X+\Delta$, where $\Delta$ is positive. I need to show that Y is stochastic bigger than X.
To show that Y is stochastic larger than X, I will use $P(Y>z)\geq P(X >z)$, which is the same as $F_Y(z) \leq F_X (z)$. I don't know how to include $Y=X+\Delta$, can anyone explain in details what to do, and which direction I should go?
Thanks in advance,