Continuous Distributions Two different kinds of "infinity"



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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

Continuous

PMF Charts

PDF Charts

To find probability = add

To find probability = take integral

Sum of all possible prob = 1

Integral of all possible prob = 1

P(X=a) = some value

P(X=a) = 0 ALWAYS

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)

CDF (Cumulative Density Function) = P(X≤x)





Draw Graphs




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= =

=





= =






Discrete

Continuous















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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