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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

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

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