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I am reading "Probability" by Pitman and in the section that talks about normal distribution sais $\Phi(0,1)=0.5\Phi(-1,1)$.

Can someone explain this equality ?

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    If it's the definition then I understand it, if it's$a$theorem then I don't understand the theorom hence I don't rally understand this statement..2012-04-11

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Let $\Phi(b)$ be the cumulative distribution function of the normalized normal distribution. That is, $\Phi(b)=P(X. Then it's convenient to introduce $\Phi(a,b)=\Phi(b)-\Phi(b)$, which expresses the probability $P(a. (Could also be written as $P(a\le X, which is the same probability because $P(X=a)=0$.) Since $X$ is symmetric, $P(0