# Difference between revisions of "Eleisha's Segment 22: Uncertainty of Derived Parameters"

(Created page with "<b> To Compute </b> 1. In lecture slide 3, suppose (for some perverse reason) we were interested in a quantity <math> f = b_3/b_5 </math> instead of <math> f = b_3b_5 </math>...") |
|||

Line 1: | Line 1: | ||

− | <b> To Compute </b> | + | <b> To Compute: </b> |

+ | |||

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

2. Same set up, but plot a histogram of the distribution of <math> f </math> by sampling from its posterior distribution (using Python, MATLAB, or any other platform). | 2. Same set up, but plot a histogram of the distribution of <math> f </math> by sampling from its posterior distribution (using Python, MATLAB, or any other platform). | ||

− | <b> To Think About </b> | + | <b> To Think About: </b> |

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? | 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? | 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? | ||

+ | |||

+ | <b>Back To: </b> [[Eleisha Jackson]] |

## Revision as of 11:28, 3 April 2014

** 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?

**Back To: ** Eleisha Jackson