Assume that X, the life of a light bulb (in years), is a continuous random varia

Question

Assume that X, the life of a light bulb (in years), is a continuous random
variable with the probability density function
fX (x)
(1/3) e^(-x/3) x > 0
0 otherwise.
(a) Find the cumulative distribution function of X.
(b) What is the median life of a light?
(c) Without evaluating the mean, would you expect the mean of the distribution to be larger
or smaller than the median? Explain.
(d) What is the probability that a light will last longer than 3 years?
(e) A string of patio lights contains 30 lights of the kind described above. The lights are
wired in series (i.e., if any light fails the whole string will go dark). The lights fail
independently of each other. What is the probability that the string of lights will work
for at least 3 years?

Explanation / Answer

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