Question

Quick Question on Uniform Distribution...Please Help!

a continuous uniform distribution has a density function of f(x)=1. the lower bound of the distribution is 3.4. The median of the distribution is: a) 3.7 b) 3.9 c) 4.0
The correct answer is B but I'm not sure how to get it. Thanks

Answer 1

anyone?

Answer 2

please help

Answer 3

The median for any continuous distribution with density \(f(x)\) and support \(\mathbb{S}\) is given by the value of \(k\in\mathbb{S}\) such that
\[\int_{\mathbb{S}^*}f(x)\,\mathrm{d}x=\frac{1}{2}\]where I'm using \(\mathbb{S}^*\) to denote the partition of the support \(\mathbb{S}\) such that \(\mathbb{S}^*=\{x\in\mathbb{S}\,|\,x\le k\}\), which in this case is to say
\[\int_{-\infty}^kf(x)\,\mathrm{d}x=\int_{3.4}^k1\,\mathrm{d}x=\frac{1}{2}\]