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5. Descriptive Statistics
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6. Information Gain and Entropy
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7. Probability and it's Uses
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8.Baye's Theorem
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9.Probability Distribution
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8.Probability Distribution
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9.Baye's Theorem
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10. Statistical Inference
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11. Hypothesis Testing
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12. Testing the Data
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P(A ∩ B) = P(A) P(B|A)
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# 8. Baye's Theorem (aka, Bayes Rule)
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# 8. Probability Distribution:
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Probability is often associated with at least one event. This event can be anything. Basic examples of events include rolling a die or pulling a coloured ball out of a bag. In these examples the outcome of the event is random (you can’t be sure of the value that the die will show when you roll it), so the **variable that represents the outcome of these events is called a random variable (often abbreviated to RV)**.
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### The 3 types of probability
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#### Marginal Probability:
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If A is an event, then the marginal probability is the probability of that event occurring, P(A).
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**Example:** Assuming that we have a pack of traditional playing cards, an example of a marginal probability would be the probability that a card drawn from a pack is red: P(red) = 0.5.
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#### Joint Probability:
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The probability of the intersection of two or more events. Visually it is the intersection of the circles of two events on a Venn Diagram (see figure below). If A and B are two events then the joint probability of the two events is written as P(A ∩ B).
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**Example:** The probability that a card drawn from a pack is red and has the value 4 is P(red and 4) = 2/52 = 1/26. (There are 52 cards in a pack of traditional playing cards and the 2 red ones are the hearts and diamonds). We’ll go through this example in more detail later.
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#### Conditional Probability:
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The conditional probability is the probability that some event(s) occur given that we know other events have already occurred. If A and B are two events then the conditional probability of A occurring given that B has occurred is written as P(A|B).
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**Example:** The probability that a card is a four given that we have drawn a red card is P(4|red) = 2/26 = 1/13. (There are 52 cards in the pack, 26 are red and 26 are black. Now because we’ve already picked a red card, we know that there are only 26 cards to choose from, hence why the first denominator is 26).
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# 9. Baye's Theorem (aka, Bayes Rule)
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Before understanding Baye's Theorem first we learn about **Conditional Probability**:
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##### Conditional Probability :
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So the "Probability of dangerous Fire when there is Smoke" is 9%
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# 9. Probability Distribution:
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# 9. Probability Distribution:
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Probability is often associated with at least one event. This event can be anything. Basic examples of events include rolling a die or pulling a coloured ball out of a bag. In these examples the outcome of the event is random (you can’t be sure of the value that the die will show when you roll it), so the **variable that represents the outcome of these events is called a random variable (often abbreviated to RV)**.
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### The 3 types of probability
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#### Marginal Probability:
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If A is an event, then the marginal probability is the probability of that event occurring, P(A).
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**Example:** Assuming that we have a pack of traditional playing cards, an example of a marginal probability would be the probability that a card drawn from a pack is red: P(red) = 0.5.
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#### Joint Probability:
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The probability of the intersection of two or more events. Visually it is the intersection of the circles of two events on a Venn Diagram (see figure below). If A and B are two events then the joint probability of the two events is written as P(A ∩ B).
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**Example:** The probability that a card drawn from a pack is red and has the value 4 is P(red and 4) = 2/52 = 1/26. (There are 52 cards in a pack of traditional playing cards and the 2 red ones are the hearts and diamonds). We’ll go through this example in more detail later.
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#### Conditional Probability:
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The conditional probability is the probability that some event(s) occur given that we know other events have already occurred. If A and B are two events then the conditional probability of A occurring given that B has occurred is written as P(A|B).
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**Example:** The probability that a card is a four given that we have drawn a red card is P(4|red) = 2/26 = 1/13. (There are 52 cards in the pack, 26 are red and 26 are black. Now because we’ve already picked a red card, we know that there are only 26 cards to choose from, hence why the first denominator is 26).
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