Notes, summaries, assignments, exams, and problems for Baccalaureate

Calculating Karl Pearson Correlation Coefficient

Question 11: Calculate the coefficient of correlation from the following data:

To calculate Karl Pearson's coefficient of correlation (r), we use the formula:

r = ∑dx·dy / √(∑dx² × ∑dy²)

Where:

• dx = X - X̄
• dy = Y - Ȳ

Step 1: Find the Means

First, calculate the mean of X (X̄) and Y (Ȳ):

X̄ = (12 + 9 + 8 + 10 + 11 + 13 + 7) / 7 = 70 / 7 = 10

Ȳ = (14 + 8 + 6 + 9 + 11 + 12 + 3) / 7 = 63 / 7 = 9

Step 2: Prepare the Calculation Table

Step 3: Substitute into the Formula

Substitute the sums from the table into the correlation formula:

r = 46 / √(28 × 84)
r = 46... Continue reading "Correlation Coefficient, Regression, and Chebyshev's Theorem" »

Credit Risk Ratios and Liquidity Metrics

Short-Term Liquidity — Stock

• Current Ratio = Current Assets / Current Liabilities (>1 is better)
• Quick Ratio = (Cash + Short-Term Investments + Receivables) / Current Liabilities
• Cash Ratio = (Cash + Short-Term Investments) / Current Liabilities

Short-Term Liquidity — Flow

• Cash Flow Ratio = Cash Flow from Operations / Current Liabilities
• Defensive Interval = (Cash + Short-Term Investments + Receivables) / Capital Expenditures × 365
• Cash Flow to Capital Expenditures = Unlevered Cash Flow from Operations / Capital Expenditures

Long-Term Solvency — Stock

• Debt to Assets = Total Debt / Total Assets
• Debt to Equity = Total Debt / Total Equity
• Long-Term Debt Ratio = Long-Term Debt / (Long-Term Debt + Equity)

Long-

Introduction to Statistical Learning

Key Notation

• Y: Response (dependent/output) variable - quantitative or qualitative
• X₁,...,Xₚ: Predictors (features/covariates/independent variables)
• p: Number of predictors
• n: Number of observations
• i: Subject index (i = 1,...,n)
• j: Variable index (j = 1,...,p)
• Data: (Yᵢ, Xᵢ), i = 1,...,n

Types of Learning

• Supervised learning: Have both Y and X (prediction or inference) - PRIMARY FOCUS
• Unsupervised learning: Have X but no Y

Model for Data

Yᵢ = f(Xᵢ) + εᵢ, i = 1,...,n
Assumptions: E(εᵢ) = 0, var(εᵢ) = σ², εᵢ are mutually independent
Properties: E(Yᵢ|Xᵢ) = f(Xᵢ), var(Yᵢ|Xᵢ) = σ²

Prediction vs Inference

2023 "Vignaverde" Grillo – Marco De Bartoli

This Grillo from western Sicily is traditionally farmed and fermented in stainless steel to maintain precision. What makes this wine interesting is not oak or technique, but its natural structure: Grillo naturally possesses a phenolic grip and distinct salinity.

• Aromas: Citrus peel, wild herbs, almond, and sea breeze.
• Profile: Mediterranean, dry, slightly textured, and highly gastronomic.

2019 Grüner Veltliner Smaragd – Gritsch

Sourced from Spitzer Graben, one of the coolest valleys in the Wachau. This wine undergoes slow fermentation in steel followed by long lees aging. While "Smaragd" denotes full ripeness and concentration, this bottling remains incredibly tight and mineral-driven.

• Flavor Profile:

Essential English Vocabulary

• Made improvements to: Hacer mejoras en
• Influencing: Influir en
• Make advances in: Hacer avances en
• Turning point: Punto de inflexión
• Transform life: Transformar
• Inspired: Inspirado
• Overcame these difficulties: Superó estas dificultades
• Remarkable achievement: Logro notable
• Seeking ways to improve: Buscar maneras de mejorar
• Considerable: Considerable, importante
• Dramatic: Dramático, radical
• Far-reaching: De largo alcance, trascendental
• Refreshing: Renovador, refrescante
• Subtle: Sutil
• Unexpected: Inesperado
• Looks back on: Recordar (el pasado)
• Stand up for: Defender (una causa, creencia)
• Get through: Superar (una dificultad)
• Miss out on: Perderse (una oportunidad, experiencia)
• Keep up with: Mantenerse al día con
• Get down with: (Coloquial)

Circular Queue Implementation Using Linked Lists

This C program demonstrates the implementation of a circular queue using a linked list structure. The queue handles integer data.

Data Structure Definition

#include <stdio.h>
#include <stdlib.h>

typedef struct QueueType {
    int Data;
    struct QueueType *Next;
} QUEUE;

QUEUE *Front = NULL; // Pointer to the front of the queue
QUEUE *Rear = NULL;  // Pointer to the rear of the queue

// Function prototypes
void Enqueue(int Num);
int Dequeue();
void DisplayQueue();
int Menu();

Enqueue Operation

The Enqueue function inserts a number into the circular queue. It handles memory allocation and maintains the circular link by ensuring Rear->Next always points to Front.

void Enqueue(int Num)

Extraction of Zinc (Zn)

Major Ores of Zinc

• Zinc blende (ZnS)
• Calamine (ZnCO₃)
• Zincite (ZnO)

Zinc is primarily extracted from calamine and zinc blende ores.

Extraction from Calamine Ore

Zinc oxide is obtained by calcining calamine:

ZnCO₃ → ZnO + CO₂↑

Zinc metal is then obtained by heating zinc oxide (ZnO) with coal powder:

ZnO + C → Zn + CO↑

Extraction from Zinc Blende

Zinc oxide (ZnO) is obtained by roasting concentrated zinc blende at high temperatures in the presence of air:

2ZnS + 3O₂ → 2ZnO + 2SO₂↑

The resulting ZnO is reduced using the carbon method described above.

Purification of Zinc

The zinc obtained is impure and is purified via electrolysis. A pure aluminum sheet serves as the cathode, while impure zinc acts as the anode in... Continue reading "Industrial Extraction Processes for Zinc and Aluminum" »

1. Ariketa

1.1. Dendak Irekitzea

18:26an ireki dituzte hainbat denda.

18:26an - hainbat denda

1.2. Anai-Arreben Jaiotza

1991ko maiatzaren 26an jaio ziren zure anai-arrebak.

Maiatzaren 26an - anai-arreba

1.3. Hizkuntza Eskola

Datorren ikasturtean hizkuntza-eskolan emango dute izena hainbat neskek.

Hizkuntza-eskolan - dute - hainbat neskak

1.4. Goizeko Irteera

Urtarriletik maiatzera, ostegunetan, goizeko 07:30etan aterako gara etxetik.

Urtarriletik maiatzera - 07:30ean

1.5. Ekonomi Bileraren Amaiera

Ekonomi-arloko bilera gaueko zortzi eta erdietan amaitu zen; proposamenaren inguruko bozketan, sei eta lau egin zuten.

Ekonomia-arloko - zortzi eta erdietan - sei eta lau egin zuten

1.6. Hezkuntza Proiektua

Ez zaitu inork ere ezagutu, hezkuntza proiektuan aritu ginenetik... Continue reading "Spanish Civil War: Causes, Consequences & Basque Impact" »

Tile Sequence Validation Logic

The following function determines if a sequence of tiles is valid by checking their compatibility and adjusting their orientation if necessary.

def is_valid_sequence(seq: list[Tile]) -> bool:
    if len(seq) < 2:
        res = True
    else:
        if not are_compatible(seq[0], seq[1]):
            seq[0] = seq[0][1], seq[0][0]
        i = 1
        while i < len(seq) and are_compatible(seq[i - 1], seq[i]):
            if seq[i - 1][1] != seq[i][0]:
                seq[i] = seq[i][1], seq[i][0]
            i += 1
        res = i == len(seq)
    return res

Square-Free Number Verification

This function checks if a positive integer is square-free, meaning no prime factor has an exponent greater than one.

def