Question

On average a light bulb can last for 500 days. Suppose the life of a light bulb follows an exponential distribution. What is the probability that the light bulb can last for another 400 days given that it has been lasted for 100 days?

0.5501

0.3679

0.0000

0.4493

Answer 1

Let X : Life of light bulb

Average life of bulb = 500 days

X ~ Exp ( mean = 500)

The probability density function of X is

e-1/500. r >0 f(x) = 500

Required Probability = P ( X >400 +100 / X > 100) = P ( X > 500 /X > 100)

By memory less property of exponential distribution

P ( X >a + b / X >a) = P ( X> a)

Hence required probability is

P(X > 400) 500e-z/soodr = [-e-z/500]400 = e-0.8 = 0.4493

Correct Answer : 0.4493