Question

The distance between flaws on a long cable is exponentially distributed with mean 12 m. Find the probability that the distance between two flaws is between 8 and 20 m (exclusive).

Answer 1

Let , X be the distance between the flaws on a long cable.

Here ,

Therefore ,

Therefore , the probability density function of X is ,

;

= 0 ; otherwise

Now ,

Therefore , the probability that the distance between two flaws is between 8 and 20 m is 0.3245.