# 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 $$a+b$$.

Inspiration

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