Math 132A

Continuous Random Variables

Types of Random Variables

• Discrete

• Continuous

Continuous Random variable

Density Curve

Probability for Continuous RV

\(\operatorname{P}(X = x) = 0\)

\(\operatorname{P}(a\le X \le b) = {}\) the area under the density curve, between \(a\) and \(b\).

\(\operatorname{P}(X \le b) = {}\) the area under the density curve, to the left of \(b\).

\(\operatorname{P}(X \ge a) = {}\) the area under the density curve, to the right of \(a\).

\(\operatorname{P}(5 \le X \le 7.5)\)

\(\operatorname{P}(X \le 5)\)

\(\operatorname{P}(X \ge 7.5)\)