Problem: The random variable T denotes the time in second for which a firework burns before exploding. The probability density function of T is given by
![551_probability density function.jpg](https://secure.tutorsglobe.com/CMSImages/551_probability%20density%20function.jpg)
Where k is a constant.
(i) Show that k = 1/5(e - 1).
(ii) Sketch the probability density function.
(iii) 80% of firework burn longer than a certain time before they explode. Find this time.
![552_Probability.png](https://secure.tutorsglobe.com/CMSImages/552_Probability.png)