The probability density function of a continuous random variable is
$\begin{equation*} f(x) = \begin{cases} \frac{3}{4}(2x - x^2), & 0 \le x < 1\\ cx, & 1 \le x < 2\\ 0, & \text{otherwise} \end{cases} \end{equation*}$
That is, $f(x)$ is defined as $\frac{3(2x - x^2)}{4}$ for $0 \le x < 1$, as $cx$ for $1 \le x < 2$, and 0 elsewhere, where $c$ is a constant. Find a lower bound for
$P(\mu - 2\sigma < X < \mu + 2\sigma)$ using Chebyshev's theorem, where $\mu$ stands for the mean and $\sigma$ stands for the standard deviation.
A) 0.5
B) 0.25
C) 0.75
D) 0.0625
E) 0.9375