Continuous Distributions
Two different kinds of “infinity”
Aleph null – countable infinity “start at 0 and just keep counting”
Aleph one – all the numbers that are missing in the gaps between integers!
Discrete
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Continuous
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PMF Charts
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PDF Charts
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To find probability = add
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To find probability = take integral
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Sum of all possible prob = 1
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Integral of all possible prob = 1
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P(X=a) = some value
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P(X=a) = 0 ALWAYS
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P(X≤a) ≠ P(X |
P(X≤a) = P(X |
CDF is also used to find probability: CDF F(X) = P(X≤a) =
Example: time it takes to eat breakfast in the morning has a PDF of:
PDF (Probability Density Function)
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CDF (Cumulative Density Function) = P(X≤x)
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Draw Graphs
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Percentiles:
In general to find percentiles set percentile to CDF and solve for x
Median (50th percentile)
Things to remember:
PDF CDF you want to integrate
CDF PDF you want to differentiate
To find probabilities using PDF – you must integrate
To Find probabilities using CDF – plug into function
To find E(X) or Var(X) use PDF
To find Percentiles use CDF
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