Let U1, U2, and U3 beindependent uniform random variables. a) Find the joint density of U1, U2, andU3. b) The locations of three gas stations are independently andrandomly placed along a mile of a highway.

Let U1, U2, and U3

beindependent uniform random variables.
a) Find the joint density of U1, U2,
andU3.
b) The locations of three gas stations are independently
andrandomly placed along a mile of a highway. What is
theprobability that no two gas stations are less than 1/3
mileapart?

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Let U1, U2, and U3 beindependent uniform random variables. a) Find the joint density of U1, U2, andU3. b) The locations of three gas stations are independently andrandomly place…

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