Notes, summaries, assignments, exams, and problems

Data Science, Machine Learning, and Artificial Intelligence

Statistical Measures and Causal Inference Concepts

Measures of Dispersion and Relationship

Variance

Variance: Estimates how far a set of numbers (random) are spread out from their mean value.

Covariance

Covariance: The relationship between two variables.

• Cov = 0: Unsure of the relationship.
• Cov > 0: Suggests Y will be above average when X is above average.
• Cov < 0: Suggests Y will be below average when X is above average.

The formula for variance is often expressed as: $\mathbb{E}[X^2] - (\mathbb{E}[X])^2$ (where $\mathbb{E}$ is the Expected Value).

The formula for covariance between two variables $X$ and $Y$ is: $\mathbb{E}[(X - \mathbb{E}[X])(Y - \mathbb{E}[Y])]$

Pearson's Correlation Coefficient

Standardizes covariance between -1 and 1:

Pearson’s

Boolean Algebra Fundamentals

Formulating Expressions: SOP and POS

Sum of Products (SOP) Formulation Steps

1. Circle rows in the truth table where the output $Y = 1$.
2. Identify the minterms corresponding to the circled rows.
3. Sum (OR) the selected minterms to form the final expression.

Product of Sums (POS) Formulation Steps

1. Circle rows in the truth table where the output $Y = 0$.
2. Identify the maxterms corresponding to the circled rows.
3. Multiply (AND) the selected maxterms to form the final expression.

Order of Evaluation in Boolean Algebra

Operations are evaluated in the following sequence:

1. Parentheses
2. NOT (Complementation)
3. AND (Multiplication)
4. OR (Addition)

Fundamental Boolean Laws and Theorems

• Identity Laws

  • $A + 0 = A$
  • $A \cdot 1 = A$

• Null Laws

  • $A + 1 = 1$
  • $A \cdot

Criteria for Selecting Distillation Equipment

• Pressure Drop: Packed towers have a lower pressure drop (1/5th to 1/8th of tray towers), making them suitable for high vacuum distillation.
• Tower Diameter: Packed towers are preferred for very small diameters (<150 mm) due to fabrication difficulties with trays, while tray towers are used for large diameters to ensure proper liquid distribution.
• Liquid-Vapor Ratio: Packed towers are suitable for high L/V ratios, while tray towers are better for very low L/V ratios due to minimum wetting rate requirements.
• Corrosive Systems: Packed towers with plastic or reinforced plastic packings are more economical than tray towers requiring special metal alloys (e.g., Hastelloy-B for methyl iodide-acetic acid

Lecture 1: Moore's Law

Moore's Law: The number of transistors on microchips doubles every two years.

Lecture 2: Logic Gates

AND, OR, and NOT gates are universal.

Logic word problem steps:

Example: In a bank, there were four employees: the bank manager, assistant manager, teller, and the security guard. The bank has a single vault for the storage of their money. This vault was designed so that it needs four signals to open it. These four signals are from the bank manager, assistant manager, teller, and the security guard. For the vault to open, it needs the following conditions:

1. No single employee can open the vault.
2. It can be opened with three employees as long as one of them is the manager.
3. It can be opened by the manager together with the assistant

1. PIC18 Architecture Details

• Harvard Architecture

  Features distinct program memory and data memory. Includes the MPU, Program Memory, Data Memory, I/O Ports, and support devices like timers.

• Microprocessor Unit (MPU)

  • ALU (Arithmetic Logic Unit)

    Performs operations such as addition, subtraction, and logical operations.

  • Registers

    Includes WREG (8-bit accumulator), Program Counter (PC), Stack Pointer (SP), and File Select Registers (FSRs).

  • Memory

    Offers 2 MB of program memory and 4 KB of data memory.

  • Bank Switching

    Data memory is divided into 16 banks, with one 256-byte access bank.

2. Data Formats and Representations

• Unsigned Integers

  These are 8-bit values, ranging from 0 to 255.

• Signed Integers

  Represented using 2's complement, with a range from -128 to

Essential Statistical & Numerical Concepts

This document covers fundamental questions and answers across various topics in statistics, numerical methods, and data analysis. Each section provides a concise explanation of key concepts.

1. What is Interpolation?

Interpolation is a mathematical technique used to estimate unknown values that fall between known data points. It involves creating a function or model based on the given data and using it to predict values within the range of the data, rather than extrapolating outside it. This method is commonly applied in fields like data analysis, engineering, and computer graphics for filling in missing data or smoothing curves.

2. Regula Falsi Method Formula for Finding Roots

The formula for finding... Continue reading "Core Concepts in Statistics and Numerical Analysis" »

Understanding Ancient Mesoamerican Civilizations

Delve into the rich history and complex structures of ancient Mesoamerican societies. This document highlights key aspects, from their societal organization and agricultural innovations to their lasting cultural and historical impact.

Key Aspects of Mesoamerican Societies

• Classic Period Decline: Societal Shifts

  An understanding of the societal, political, and economic shifts following the Classic period is crucial to grasp its consequences.

• Monumental Architecture and Social Hierarchy

  Analyzing how the construction of large-scale structures reveals the power structures and social hierarchies within Mesoamerican societies.

• Mesoamerican Calendars: Culture and Daily Life

  Explaining the importance of the

Software Engineering and Processes

Agile Manifesto

• Individuals/Interactions over Processes
• Working software over documentation
• Collaboration over negotiation
• Responding to change over following a plan

Requirements Engineering

Descriptions of the services that a system should provide and the constraints on its operation.

Functional

What the system should do.

Non-functional

Not directly concerned with the specific services delivered by the system to its users.

Quality Attributes

A scenario describing quality attributes typically involves these elements:

1. Source: Origin of the stimulus.
2. Stimulus: The event arriving.
3. Artifact: Where the event arrives.
4. Environment: Conditions in which the scenario takes place.
5. Response: The result of the event.
6. Response Measure: Must