Visualization: The world map resized by population

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,

Visualization: Worldwide Internet Usage

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?)

Logic NAND equivalence

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,...

The fundamental desiderata of Probability Theory

Name the three fundamental desiderata of Probability Theory.

Probability Theory: correspondence with commonsense

Show via an example Venn diagram that if, holds, then, also holds.

The proof of Bayes' Rule via Venn diagram

Prove the Bayes’s rule via Venn diagrams, \[\pi(B|A) = \frac{ \pi(A|B) ~ \pi(B) } { \pi(A) } ~.\]

The fundamental logical operators

Show that the following identities hold, where the two arrow-up and arrow-down symbols represent the fundamental NAND and NOR operators,

Logic functions in terms of logic functions

Show that the following functions, can be written as, where the basis logic functions have the following truth table,

Logic functions with 2 input

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.

Logic functions with 1 input

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...

The two types of scientific reasoning

Name the two types of scientific reasoning and give an example argument for each one.

Logical product denial

Show via Venn diagrams that the negation of a logical product ($\overline{AB}$) is equivalent to the logical sum of the negations ($\bar{A}+\bar{B}$).

Policeman, jewelry, and burglar

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...

Logical implication

Show via Venn diagrams that the logical implication ($A\Rightarrow B$) is equivalent to the following expressions, \[A\bar{B} ~ \text{is false} ~,\] \[\bar{A} + B ~ \text{is true} ~,\] \[A = AB ~,\]

Logic implication, denial, equivalence

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...

Venn diagram representation of Boolean expressions

Consider the following Boolean algebraic expressions. Draw a Venn diagram corresponding to each one,

Regression: Predicting the bivariate distribution of the a dataset subjected to censorship (sample incompleteness)

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...

Regression: Predicting the distribution of the a dataset subjected to censorship (sample incompleteness)

Problem Supposed we have observed a dataset comprised of $15027$ events with one attribute variable in this file: data.csv. Plotting these points would yield a red-colored histogram like the following plot, The pale black shaded area represents the missing points...

Best visualization coloring

Problem Consider the following color palettes. Which one is more appropriate for effective visualization communications with humans?