[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 at random a real number

[math]X[/math] from the interval [math][2,10][/math].

• Find the density function [math]f(x)[/math] and the probability of an event [math]E[/math] for this experiment, where [math]E[/math] is a subinterval [math][a,b][/math] of [math][2,10][/math].
• From (a), find the probability that [math]X \gt 5[/math], that [math]5 \lt X \lt 7[/math], and that [math]X^2 - 12X + 35 \gt 0[/math].