Segment 22. Uncertainty of Derived Parameters

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To Compute

1. In lecture slide 3, suppose (for some perverse reason) we were interested in a quantity Failed to parse (unknown error): f = b_3/b_5 instead of Failed to parse (unknown error): f = b_3b_5 . Calculate a numerical estimate of this new Failed to parse (unknown error): f and its standard error.

2. Same set up, but plot a histogram of the distribution of Failed to parse (unknown error): 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?