Brilliant - Predictions and Probability Flashcards

1
Q

What is the assumption we make when dealing with predictions?

A

That the future will behave like the past.

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2
Q

What does the number of times an outcome appears in our data set directly relate to?

A

It directly relates to how likely it is to happen again in the future.

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3
Q

What is a probability?

A

The number of times an event appears in a dataset divided by the total number of records.

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4
Q

What is a Probability Mass Function (PMF)?

A

It lists the probabilities for all events.

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5
Q

What is normalization?

A

When you rescale a bar chart by the total height.

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6
Q

How do we handle any new information?

A

We ignore data that doesn’t match the conditions.

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7
Q

What does the joint probability P9A and B) measure?

A

It measures the chance the two events A and B will happen together.

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8
Q

How are joint and conditional probabilities connected?

A

They are connected through P(A and B) = P(A|B) * P(B)

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9
Q

What is the Law of Total Probability?

A

If the data splits with no overlap between B₁ and B₂, we have: P(A|B₁) * P(B₁) + P(A|B₂) * P(B₂).

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10
Q

What does the Law of Total Probability allow us to do?

A

It lets us update our probabilities when filtering isn’t an option.

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11
Q

What is Bayes’ Rule?

A

P(A|B) = P(B|A) * [P(A)] / [P(B)]

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12
Q

What does Bayes’ Rule allow us to do?

A

It allows us to update probabilities in light of new evidence.

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13
Q

What is the Cumulative Distribution Function (CDF)?

A

P(X ≤ x); the CDF accumulates the PMF values–if X is a random quantity, P(X ≤ x) is the sum of all the PMF values up to and including the one for x.

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14
Q

What happens to the CDF if x becomes negative?

A

Then CDF(x) drops to 0.

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15
Q

What happens to the CDF when x is big enough?

A

Then CDF(x) is the sum of all the PMF values, so it has to be 100%.

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16
Q

What do the cumulative sums in the CDF(X ≤ x) generally do?

A

They generally smooth out the noise in the PMF P(X = x).