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Question regarding geometric distribution

Suppose that X is a geometric random variable. (a) prove that for positive integers n and k, P(X=n+k|X>n)=P(X=k). (b)explain what this result means and why it makes sense for a geometric distribution to have this property.

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## Q : Population of filling volumes

A bottled water plant utilizes a production process designed to fill bottles with 20 ounces of water. The population of filling volumes is normally distributed with a standard deviation of 1.3 ounces.