Statistical Mechanics. Carefully explain. Consider an ideal gas of N molecules, contained in a volume V0 and in thermody

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Statistical Mechanics. Carefully explain.
Consider an ideal gas of N molecules, contained in a volume V0 and in thermodynamic equilibrium. Let n be the number of molecules located within a subvolume V of V0. The probability that a molecule is inside V is p = V/V0.
a) What is the average number <n> of molecules inside V? express this number as a function of (N, V0, V).
b) Calculate the standard deviation, σ, in the number of molecules contained in V and calculate the deviation σ/<n> as a function of (N, V0, V).
c) Calculate the limit of the answer of b) when V<< V0
d) What is the value of σ if V → V0? Does the answer to b) agree with this value?