Question

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

- Find the probability that the distance between two flaws is greater than 15 m.
- Find the probability that the distance between two flaws is greater than 25 m given that it is greater than 10 m.
- 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**

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