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Summary Intro to probability distributions $5.52
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Summary

Summary Intro to probability distributions

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An intro to concepts relating to probability distributions.

Preview 2 out of 8  pages

  • No
  • Chapter 4 to 6
  • June 18, 2023
  • 8
  • 2022/2023
  • Summary
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Quantiles
smallest
Example:the 90th percentile (0.9th quantile) is the
number such

thatP1 X the number) > 0.9.




pth ele

This is the
↓ These are
population A quail
-


quantiles.

sample percentiles

pi
y)+17 (
=
↑Holy
quantiles:

-


①p


What's the difference between percentiles and quantiles?
Quantiles will be decimals
(e.g. 0.5th quantile) whereas percentiles will be

the quantile 100
x
(eg. 50th percentile).


Normal Distribution



pdf fy(y)
tep( z(y-M(]j
>
=
-



a
c
-
-




# ai2 ( z(-+ y]/ -

, Uniform distribution




(ar0
oz e
For X -unif (0,02):fx(x) =




otherwise

Fx(x)
2 -




Op
formula.
=

think
- ofthe linear interpolation
O2-0,


E(x) P,
VarIX)=(O-d
0,
=


+



-
average




8
for e
Y-gamma(a.), fy(y)
-




Gamma distribution -
y
=




,y>0
BYT(x)
Note thatP (x) (a -1)! (x 1)4(x 1)!
=


= -
-




E(Y) =
a
B and Var(Y) a
=



&2

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