The life X, of the StayBrite light bulb is modelled by the probability density function$$f(x) = \left(\begin{matrix}2e^{-2x} \ 0\end{matrix}\right)$$$$x \ge 0 -otherwise- $$Where x is measured in thousands of hours.

(a) Sketch the graph of f(x).
(b) Find the median life of these StayBrite bulbs

(b) E.g. $$P(X \le M) = \int\limits_{-\infty}^{M} f(x)dx= {1\over2}$$

Question

The life X, of the StayBrite light bulb is modelled by the probability density function$$f(x) = \left(\begin{matrix}2e^{-2x} \ 0\end{matrix}\right)$$$$x \ge 0 -otherwise- $$Where x is measured in thousands of hours.

(a) Sketch the graph of f(x).
(b) Find the median life of these StayBrite bulbs 

(b) E.g. $$P(X \le M) = \int\limits_{-\infty}^{M} f(x)dx= {1\over2}$$

escherichiarinku · Answer

|dw:1328093870926:dw| There's nothing for x<0, because your function is defined for x>=0. Don't forget that! this is, by the way, a case of http://en.wikipedia.org/wiki/Exponential_distribution