Looks like the next one’s here. It can be fun, you know. If you aren’t afraid of all those marks and test scores. Try to like just 1 problem from here. It works wonders inside the mind. As always, make sure to have your id’s next to the paper when you submit. This one’s needs to be starting grading by July 1, 2021.
Question 1
Suppose a person walks 3 meters to the store for some tea. Is this walk time dependent? Does the person taking a longer time change the distance they travelled? Or does this change the speed? Is it reasonable to assume a steady speed for walking? Why or why not? Now, suppose they walk with you only knowing their starting point and end point; is this walk time dependent?
Question 2
Along the real line classically described in mathematics or $\mathbb{R}$, the range of numbers goes in infinity in both directions. Consider a small subset of it: $S = [0,1]$. Does this subset go to infinity in both directions? How about when we approach 1? 0? Consider a different one, $S^* = (0,1)$. Does this one even include 0 or 1?
Question 3
In statistics we describe the average of a set of random observations as $\bar{X}$. If the observations are random, does this mean that $\bar{X}$ will be random too? Does randomness in this case imply we know the distribution of the quantity but not the quantity itself? Bill is comparing test scores between his class and Jill’s class. Would an average alone be enough to see who scores higher, and if we did use the average; what information does it tell us? Is it enough to say, Bill is more effective?
(this is just an illustration).