Suppose X ~ N(0,1).

Why can we write P(a≤ X ≤ b) = P(X ≤ b) – P(X ≤ a)

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- Jun 23rd 2011, 11:07 AMKanwar245Normal Distribution
Suppose X ~ N(0,1).

Why can we write P(a≤ X ≤ b) = P(X ≤ b) – P(X ≤ a) - Jun 23rd 2011, 11:59 AMPlatoRe: Normal Distribution
To really answer your question, we need to know how much you understand about continuous distributions.

For example do you understand that for any, $\displaystyle \mathcal{P}(X=a)=0~?$*a*

From that it follows at once that $\displaystyle \mathcal{P}(X\le a)=\mathcal{P}(X<a).$

So $\displaystyle \mathcal{P}(X\ge a)=1-\mathcal{P}(X<a)=1-\mathcal{P}(X\le a)$.

Thus $\displaystyle =\mathcal{P}(a\le X \le b)=\mathcal{P}(X\le b)-\mathcal{P}(X\le a)$.