How is $ P(-\sqrt{y} \leq X \leq \sqrt{y}) = P(X \leq \sqrt{y}) - P(X < -\sqrt{y})$?
I recently started studying elementary statistics and I stumbled upon this in my book:
But I dont understand how $ P(-\sqrt{y} \leq X \leq \sqrt{y}) = P(X \leq \sqrt{y}) - P(X < -\sqrt{y})$. Could you help me understand what is happening here?
Attempt to understand:
$ P(-\sqrt{y} \leq X \leq \sqrt{y}) = P((-\sqrt{y} \leq X) \ \cap \ (X\leq \sqrt{y}))$ but I dont understand how AND ( $\cap$ ) becomes minus or plus here.
I know that: $$ F_X(x) = P(X \leq x) $$ Where F is cumulative distribution function. X is random variable and P is probability.
This picture illustrates what was said in the comments to your question. Let $z=\sqrt{y}$.