# It's getting a bit crowded in here

Calculus Level 5

Suppose $$9$$ real numbers are chosen uniformly and at random from the interval $$[0,1]$$. Let $$W$$ be the variable measuring the (magnitude of the) difference between the greatest and least of the $$9$$ randomly chosen numbers.

If the expected value $$E[W] = \dfrac{a}{b}$$, where $$a, b$$ are positive coprime integers, then find the product $$a*b$$.

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