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A buried treasure is believed to be somewhere on a 6-mile long ancient path. I conjecture that the density for its location T is f(t)

A buried treasure is believed to be somewhere on a 6-mile long ancient path. I conjecture that the density for its locationTisf(t) = t(6 - t)/36for0 T 6

What is the probability that it is more than 4 miles along the path?

What is the expected value of its location?

What is the standard deviation of its location?

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