(a) x can have any value on [1,4]. For f(x) to be a p.d.f., then the total area under it should

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(a) \( x \) can have any value on \( [1,4] \). For \( f(x) \) to be a p.d.f., then the total area under it should equal 1 , that is \[ \int_{1}^{4} f(x) \mathrm{d} x=1, \quad \int_{1}^{4} f(x) \mathrm{d} x=\int_{1}^{4} \frac{1}{2 \sqrt{x}} \mathrm{~d} x=[\sqrt{x}]_{1}^{4}=1 \]