[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Suppose you choose a real number [math]X[/math] from the interval

[math][2,10][/math] with a density function of the form

[[math]] f(x) = Cx\ , [[/math]]

where [math]C[/math] is a constant.

• Find [math]C[/math].
• Find [math]P(E)[/math], where [math]E = [a,b][/math] is a subinterval of [math][2,10][/math].
• Find [math]P(X \gt 5)[/math], [math]P(X \lt 7)[/math], and [math]P(X^2 - 12X + 35 \gt 0)[/math].