Question: 3. [10 points total] Consider the variance o} = (f()) - (f(u)) of an arbitrary real function f(u) of the speed v, where the average

3. [10 points total] Consider the variance o} = (f()) -

3. [10 points total] Consider the variance o} = (f()) - (f(u)) of an arbitrary real function f(u) of the speed v, where the average (f(n)) is defined as (f(v)) = $ dv f(b)G(v), f Gu where G(v) is the probability density of the speed. (a) (5 points) Show that of > 0. (Hint. consider the quantity f(u) (f(n))}] (b) (5 points) Using this result, show that (v2P) (UP)for any positive integer p

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