3 Continuous Random Variables

For a continuous random variable \(X\) with density \(f\), the expected value is again, exactly the mass of the density.

• Recall that expected values are properties of .
• Note the average of random variables is its self a random variable, and its associated distribution has an expected value.
• The center of this distribution is the same as that of the original distribution.

Sensitivity: \(P(+|Preg) = 0.75\) Specificity: \(P(-|Preg^C)~~0.52\le0.75\) \(P(Preg)=0.3\)

\[P(Preg|+) = \frac{P(+|Preg)P(Preg)}{P(+|Preg)P(Preg)~~+~~P(+|Preg^C)P(Preg^C)}\] \[P(Preg|+) = \frac{0.75(0.3)}{0.75(0.3)~~+~~(1-0.52)(0.7)}\]