Let [math]T[/math] be a random variable with range [math][0,\infty][/math] and [math]f_T[/math] its density function. Find [math]\mu(T)[/math] and [math]\sigma^2(T)[/math] if, for [math]t \lt 0[/math], [math]f_T(t) = 0[/math], and for [math]t \gt 0[/math],

• [math]f_T(t) = 3e^{-3t}[/math].
• [math]f_T(t) = 9te^{-3t}[/math].
• [math]f_T(t) = 3/(1 + t)^4[/math].