Segment 22. Uncertainty of Derived Parameters

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{{#widget:Iframe |url=http://www.youtube.com/v/ZoD3_rov--w&hd=1 |width=800 |height=625 |border=0 }}

The direct YouTube link is http://youtu.be/ZoD3_rov--w

Links to the slides: PDF file or PowerPoint file

Problems

To Compute

1. In lecture slide 3, suppose (for some perverse reason) we were interested in a quantity Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f = b_3/b_5} instead of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f = b_3b_5} . Calculate a numerical estimate of this new Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} and its standard error.

2. Same set up, but plot a histogram of the distribution of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} by sampling from its posterior distribution (using Python, MATLAB, or any other platform).

To Think About

1. Lecture slide 2 asserts that a function of normally distributed RVs is not, in general, normal. Consider the product of two independent normals. Is it normal? No! But isn't the product of two normal distribution functions (Gaussians) itself Gaussian? So, what is going on?

2. Can you invent a function of a single normal N(0,1) random variable whose distribution has two separate peaks (maxima)? How about three? How about ten?