Question

The distance between flaws on a long cable is exponentially distributed with a mean of 12 m.

1. Find the probability that the distance between two flaws is greater than 15 m.
2. Find the probability that the distance between two flaws is greater than 25 m given that it is greater than 10 m.
3. Find the probability that the distance between two flaws is greater than 20 m given that it is greater than 10 m.

Answer 1

here for exponential distribution parameter β = 12

a)

probability that the distance between two flaws is greater than 15 m:

P(X>15)=1-P(X<15)=1-(1-exp(-15/12))=

0.2865

b)

  probability that the distance between two flaws is greater than 25 m given that it is greater than 10 m:

P(X>25|X>10) =P(X>25)/P(X>10) =exp(-25/12)/exp(-10/12) =exp(-15/12)=0.2865

c)

probability that the distance between two flaws is greater than 20 m given that it is greater than 10 m. :

P(X>20 |X>10) =P(X>20)/P(X>10)=exp(-20/12)/exp(-10/12) =exp(-10/12)=0.4346