Lesson 5.2: Probability & Probability Distributions (Normal, Binomial, Poisson)
Probability is the measure of how likely an event is to occur.
It ranges from 0 to 1:
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0 → Impossible event
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1 → Certain event
🔹 Probability Distributions
A probability distribution shows how probabilities are assigned to different outcomes of a random variable.
There are many types, but in data science, three are very common:
1️⃣ Normal Distribution (Bell Curve)
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Symmetrical, bell-shaped curve.
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Mean = Median = Mode (all same at the center).
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Most data lies near the mean, fewer data points at extremes.
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Example: Heights of people, exam scores, IQ levels.
2️⃣ Binomial Distribution
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Used for experiments with two possible outcomes (Success/Failure, Yes/No).
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Example: Tossing a coin 10 times and counting the number of heads.
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Formula involves nCr, probability of success (p), failure (q = 1-p).
3️⃣ Poisson Distribution
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Used when we count number of events in a fixed time or space.
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Example: Number of emails received per hour, number of cars crossing a bridge in 1 minute.
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Events happen independently and with a known average rate (λ).
✅ Quick Recap:
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Normal → Continuous, natural data (bell curve).
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Binomial → Discrete, success/failure situations.
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Poisson → Discrete, count of events over time/space.
