Exercise L1-2 (Calculate Empirical Statistics): The previous exercise demonstrat

Question

Exercise L1-2 (Calculate Empirical Statistics): The previous exercise demonstrated that a data set
can be processed to approximate the PDF for the experiment whose repeated trials led to that data, and
that this approximation improves as the data set grows large. It should thus not be surprising that the
analogous convergence also typically occurs for any statistic derived from the PDF. This exercise explores
this phenomenon considering the second-order statistics and both the uniform distribution and the normal
distribution, relying on so-called error-bar plots to visualize these statistics.

Consider a random variable X with uniform PDF U(?, ?) as defined in (2). Verify analytically that the
mean and variance are, respectively,

(b) Consider a random variable X with normal PDF N(

Explanation / Answer

The Uniform Distribution

A continuous random variable X which has probability density function given by:

f(x) = 1 for a

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