Question

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.1. What isthe conditional probability that a repair takes at least 10 hours, given that it takes more than 8 hours?

Answer 1

Answer:

Step-by-step explanation:

Given that the time  (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.1.

Let X be the time taken for a repair

The conditional probability that a repair takes at least 10 hours, given that it takes more than 8 hours

= P(X≥10/x>8)

=$\frac{1-F(10)}{1-F(8)}$

Parameter = 0.1

F(10) = $1-e^{-1} =1-0.6321\\=0.3679$

F(8) = $1-e^{-0.8} \\=0.551$

Hence answer  =0.8187