# Normal Distribution

• June 23rd 2011, 11:07 AM
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, 11:59 AM
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)

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