Introduction to Discrete & Continuous Probability Distributions

  ✅ 1. What is a Probability Distribution? A probability distribution describes how probabilities are distributed over the values of a random variable . Random Variable : A variable whose values are outcomes of a random phenomenon. ๐Ÿงฎ 2. Types of Probability Distributions Type Description GIS Example Discrete           Takes countable values  Number of landslides per year in a          valley Continuous          Takes infinite values over an                 interval Rainfall (mm), elevation, temperature  ๐Ÿ“Œ Discrete Probability Distributions ๐ŸŽฏ 3. Binomial Distribution ✅ Definition : Used when an experiment is repeated n times , and each trial has two outcomes : success or failure. ✅ Conditions : Fixed number of trials (n) Only two possible outcomes per trial (success/failure) Constant probability of success (p) Trials are in...

Reasoning and approaches of reasoning

 


๐Ÿง  What is Reasoning?

Reasoning is the mental process of drawing conclusions from facts, observations, or assumptions.
In both animal science and economics, the way we reason determines how we:

  • Analyze problems

  • Test hypotheses

  • Interpret data

  • Make decisions

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There are three primary types of reasoning approaches:

  1. Deductive reasoning

  2. Inductive reasoning

  3. Abductive reasoning


1️⃣ Deductive Reasoning: From General to Specific

๐Ÿ” Definition:

Deductive reasoning starts with a general principle or theory and applies it to a specific case to reach a logically certain conclusion.

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✔️ Structure:

If A is true, and B fits A, then B must be true.

๐Ÿ„ Animal Science Example:

  • Premise 1: All ruminants have a four-chambered stomach.

  • Premise 2: Cows are ruminants.

  • ➡️ Conclusion: Cows have a four-chambered stomach.

๐Ÿ’น Economics Example:

  • Premise 1: When demand increases and supply remains constant, prices rise.

  • Premise 2: Demand for wheat has increased.

  • ➡️ Conclusion: Wheat prices will rise (assuming supply is unchanged).

๐ŸŽฏ Use:

Deductive reasoning is common in:

  • Scientific theories

  • Policy frameworks

  • Lab protocols and standards

  • Economic modeling


2️⃣ Inductive Reasoning: From Specific to General

๐Ÿ” Definition:

Inductive reasoning involves drawing general conclusions based on specific observations. The conclusion is probable, not guaranteed.

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✔️ Structure:

Observe → Identify a pattern → Form a general rule

๐Ÿ” Animal Science Example:

  • Observation 1: Hens on farm A produce more eggs with organic feed.

  • Observation 2: Hens on farm B also show higher egg production with organic feed.

  • ➡️ Conclusion: Organic feed may increase egg production.

๐Ÿ“ˆ Economics Example:

  • Observation 1: Lower interest rates led to increased investment in country X.

  • Observation 2: The same happened in country Y.

  • ➡️ Conclusion: Lower interest rates probably stimulate investment.

๐ŸŽฏ Use:

Inductive reasoning is used in:

  • Data analysis

  • Field observations

  • Market research

  • Hypothesis formation

  • Policy evaluation


3️⃣ Abductive Reasoning: Best Explanation

๐Ÿ” Definition:

Abductive reasoning starts with an incomplete set of observations and tries to find the most likely explanation.

It’s the logic we often use in diagnosing problems.

✔️ Structure:

You observe something surprising → Ask: “What’s the most likely cause?”

๐Ÿ• Animal Science Example:

  • Observation: A group of animals shows signs of dehydration, but water is available.

  • ➡️ Hypothesis: The water source might be contaminated or unpalatable.
    (You didn’t observe the cause directly, but infer the most likely explanation.)

๐Ÿฆ Economics Example:

  • Observation: A sharp decline in consumer spending in one region.

  • ➡️ Possible Explanation: Maybe a sudden policy change, unemployment, or inflation shock.

๐ŸŽฏ Use:

Abductive reasoning is commonly used in:

  • Veterinary diagnosis

  • Behavioural analysis

  • Economic forecasting

  • Crisis response

  • Detecting unseen causes from observed effects


๐Ÿงญ Comparison Table

FeatureDeductive ReasoningInductive ReasoningAbductive Reasoning
DirectionGeneral → SpecificSpecific → GeneralObservation → Most likely explanation
Conclusion certaintyAlways true if premises are trueProbably truePossibly true
Common use in scienceTheoretical modelsData collection & hypothesisDiagnosing & explaining anomalies
Common use in economicsPolicy logic and assumptionsEmpirical studiesInterpreting market shocks


๐Ÿงช Why This Matters in Animal Science & Economics

Animal ScienceEconomics
Testing biological theories (deductive)        Applying economic models (deductive)
Field studies on livestock (inductive)       Trend analysis and forecasting (inductive)
Diagnosing animal diseases (abductive)       Explaining inflation or poverty spikes (abductive)

✅ Summary

  • Deductive: Moves from general rules to specific conclusions – good for testing established theories.

  • Inductive: Builds general ideas from specific data – great for discovery and research.

  • Abductive: Provides the best explanation when not all facts are known – essential for problem-solving.

๐Ÿ’ก No one method is “better” — they are complementary. Real-world decision-making often combines all three.

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