The distance between major cracks in a highway follows an exponential distribution with a mean of 5 miles. X = distance between major cracks in miles. X is an exponential random variable with cracks/mile. a) What is the probability that there are no cracks in a 10 mile stretch? b) What is the probability that there are 2 cracks in a 10 mile stretch? c) What is the standard deviation of the distance between cracks? d) What is the probability that the first major crack occurs between 12 & 15 miles? e) What is the probability that there are no major cracks in two separate 5 mile stret

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f) Given no cracks in first 5 miles, what is probability that there are no cracks in the next 10 miles?

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