These self-assessment problems accompany the mini course Local measures of precision, and measures in one dimension.
In class we discussed precision vs. accuracy and, in doing so, we looked at four instances: a, b, c, and d. Then I asked you whether b or c was better. And whether b or d was better.
In both cases we answered that “it depends”. Explain why this is. Provide supporting examples for each case.
Before this topic we had looked at a handful of so-called “standard” measures of precision.
a) Name the measures we saw
b) Explain the meaning of the term “standard”
For random variable that is normally distributed:
a) What confidence level corresponds to ?
b) What confidence level corresponds to ?
c) What confidence level corresponds to ?
d) How many ‘s correspond to a 95% confidence level?
e) How many ‘s correspond to a 50% confidence level?
Sketch each of the above cases and include appropriately shaded areas and labeling of the key values and probabilities
What is the “multiplier”, , in each of the above cases? Describe in words the meaning of this multiplier and why we need it.
Imagine you do a leveling survey and a subsequent adjustment to estimate the heights of three points,
And imagine that your least squares estimate yields the following variance-covariance matrix of the adjusted unknowns in units of :
a) What is the Linear Error Probable (LEP) for each point?
b) What is the standard deviation for each?
c) Assuming a normal distribution, which of the estimated heights would be acceptable if the 3- error limit in height was 2.00 mm?
Imagine that your least squares estimate of the coordinates of 15 points yields a variance-covariance matrix of the adjusted unknowns. A subset of that matrix is given below for just the heights of points 4 and 9 in units of :
a) Provide a measure of uncertainty in height for point 4 at the 95.4% confidence level
b) Provide a measure of uncertainty in height for point 9 at the 95.4% confidence level
c) What is the meaning of the 95.4% confidence level?
d) Provide a measure of the relative uncertainty for the heights of points 4 and 9 at the 95.4% confidence level
e) Is a measure of uncertainty or relative uncertainty more meaningful? Explain.