# Normal Distribution

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• June 23rd 2011, 12:07 PM
Kanwar245
Normal Distribution
Suppose X ~ N(0,1).
Why can we write P(a≤ X ≤ b) = P(X ≤ b) – P(X ≤ a)
• June 23rd 2011, 12:59 PM
Plato
Re: Normal Distribution
Quote:

Originally Posted by Kanwar245
Suppose X ~ N(0,1).
Why can we write P(a≤ X ≤ b) = P(X ≤ b) – P(X ≤ a)

To really answer your question, we need to know how much you understand about continuous distributions.
For example do you understand that for any a, $\mathcal{P}(X=a)=0~?$
From that it follows at once that $\mathcal{P}(X\le a)=\mathcal{P}(X
So $\mathcal{P}(X\ge a)=1-\mathcal{P}(X.

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