If X is a geometric random variable, show analytically that

P{X=n+k|X>n}=P{X=k}

Using the interpretation of a geometric random variable, give a verbal argument as to why the preceding equation is true.

If X is a geometric random variable, show analytically that

P{X=n+k|X>n}=P{X=k}

Using the interpretation of a geometric random variable, give a verbal argument as to why the preceding equation is true.