Find the conditional density functions for the following experiments.

• A number [math]x[/math] is chosen at random in the interval [math][0,1][/math], given that [math]x \gt 1/4[/math].
• A number [math]t[/math] is chosen at random in the interval [math][0,\infty)[/math] with exponential density [math]e^{-t}[/math], given that [math]1 \lt t \lt 10[/math].
• A dart is thrown at a circular target of radius 10 inches, given that it falls in the upper half of the target.
• Two numbers [math]x[/math] and [math]y[/math] are chosen at random in the interval [math][0,1][/math], given that [math]x \gt y[/math].