That way and this

Calculus Level 4

A particle starts at the origin of \(3-D\) space and moves \(x\) units in the direction of \(x\)-axis,\(y\) units in the direction of \(y\)-axis and \(z\) units in the direction of \(z\)-axis. Where \(x,y,z\) are non-negative real numbers, \(x+y+z=10\). The value of \(x\) is chosen randomly from \([0,10]\), but the value of \(y\) is chosen randomly from \([0,10-x]\). Find the expected value of the square of the final displacement of the particle from the origin. If the answer is of the form \(\frac{a}{b}\), where \(a,b\) are co prime natural numbers, input \(a+b\).

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