Can you find a conditional probability value from a CDF? If so, how?
$F(x)=[x^2-4; 0<=x<1 [ x; 1<=x<2$
how to find $P[x>1/2 | x<2]$
$\endgroup$1 Answer
$\begingroup$You just have to use the definition of conditional probability, i.e.:
$$P(A|B)=\frac{P(A,B)}{P(B)}$$
so in your case:
$$P(X>\frac{1}{2}|X<2)=\frac{P(X>\frac{1}{2},X<2)}{P(X<2)}=\frac{P(\frac{1}{2}<X<2)}{P(X<2)}=\frac{F(2)-F(\frac{1}{2})}{F(2)}$$
Actually I do not really understand what is your CDF from your post, but you can compute the result now.
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