An electrical power line connecting Miami to Key largo which is48 miles long has been...

An electrical power line connecting Miami to Key largo which is 48 miles long has been cut at some random point so that the distance between the cut-point from Miami, X, can be assumed to have a uniform distribution. Find the probability that distance between the cut-point and Miami is more than 4 times the distance between the cut-point and the key Largo.

Expert Solution

We are given that the distance between the cut-point from Miami, X ~ Uniform(0,48) ; X in miles.

Thus, the distance between the cut-point from key Largo will be (48 - X) miles.

Now, since X ~ Uniform(0,48); thus the pdf of X is given by:

Therefore, the cdf of X is given by:

Now, we need to find the probability that the distance between the cut point and Miami,i.e, X, is more than 4 times the distance between the cut-point and key Largo,i.e., 48-X, which is :

which is the required answer.

orchestra answered 2 years ago

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