(Solved): The probability density function of a continuous random variable is given by \[ f(x)=\frac{1}{6} e^ ...

The probability density function of a continuous random variable is given by \[ f(x)=\frac{1}{6} e^{-\frac{1}{6} x} \text { for }[0, \infty) \] a) Find \( P(X>3) \). b) Find the mean of \( \mathrm{X} \). c) Find the CDF (cumulative distribution function). d) Use the CDF to find the median of \( \mathrm{X} \).