Problem The following plot is a refined map of the worldwide population. What kind of visualization and map is this plot? Select all that apply. Robinson map, Interrupted Goode Homolosine map, Cartesian Longitude and Latitude map, Cartogram Heat map, Winkel...
Problem The following plot uses (distorts) the country sizes to represent the worldwide population. What kind of visualization (map) is this plot? Cartogram Heat map, Robinson map, Winkel map, Choropleth, Cartogram,
Problem The following plot shows the worldwide usage of Internet by countries. What kind of visualization is this plot? (By the way, which country is the largest Internet-user in the world?)
We have learned that, \[\begin{eqnarray} \bar{A} &=& A \uparrow A ~, \nonumber \\ AB &=& (A \uparrow B) \uparrow (A \uparrow B) ~, \nonumber \\ A + B &=& (A \uparrow A) \uparrow (B \uparrow B) ~, \nonumber \end{eqnarray}\] Now,...
Name four major schools of Probability Theory.
Name the three fundamental desiderata of Probability Theory.
Show via an example Venn diagram that if, holds, then, also holds.
Prove the Bayes’s rule via Venn diagrams, \[\pi(B|A) = \frac{ \pi(A|B) ~ \pi(B) } { \pi(A) } ~.\]
Show that the following identities hold, where the two arrow-up and arrow-down symbols represent the fundamental NAND and NOR operators,
Show that the following functions, can be written as, where the basis logic functions have the following truth table,
Consider the following special functions that are TRUE only at specific points within the logical sample space: Show that the above truth table is equivalent to the following logical operations.
Consider a set of logic functions \(\{ f_1(A), f_2(A), f_3(A), f_4(A)\}\) that take a proposition (\(A\)) as input which is either True or False. These functions map the truth value of the input proposition to either True or False according...
Name the two types of scientific reasoning and give an example argument for each one.
Show via Venn diagrams that the negation of a logical product ($\overline{AB}$) is equivalent to the logical sum of the negations ($\bar{A}+\bar{B}$).
Suppose some dark night a policemanwalks down a street, apparently deserted. Suddenly he hears a burglar alarm, looks across the street, and sees a jewelry store with a broken window. Then a gentleman wearing a mask comes crawling out through...
Show via Venn diagrams that the logical implication ($A\Rightarrow B$) is equivalent to the following expressions, \[A\bar{B} ~ \text{is false} ~,\] \[\bar{A} + B ~ \text{is true} ~,\] \[A = AB ~,\]
We have learned that the logical implication ($C\Rightarrow D$) is equivalent to the following expressions, \[C\bar{D} ~ \text{is false} ~,\] \[\bar{C} + D ~ \text{is true} ~,\] \[C = CD ~,\] Now, using the above expressions, show that if, \[(B\Rightarrow...
Show, via Venn diagrams, that the following Boolean algebraic identities hold.
Show, via Truth Tables, that the following Boolean algebraic identities hold.
Problem Supposed we have observed a dataset comprised of $4975$ events with two attributes variable1 and variable2 points in this file: data.csv. Plotting these points would yield a scatter plot like the red points in the following plot, The pale...