Stat 130 – Intro to Math Stat for CS Chapter 4 Reviewer
Parameter - constant that determines the specific form of the density function Parameter Space - set of all possible values that the parameter can take on Discrete Distributions 1. Discrete Uniform Distribution -
-> đ??¸(đ?‘Ľ) =
đ?‘Ľ âˆź đ??ˇ âˆŞ (đ?‘ ) 1
pmf: đ?‘ƒđ?‘Ľ (đ?‘Ľ) = đ??ź{1,2,...,đ?‘ } 2
2
đ?‘ +1 2
-> đ?‘‰đ?‘Žđ?‘&#x;(đ?‘Ľ) =
đ?‘ 2 −1 12
2. Poisson Distribution - Model for the # of occurances of a certain event (usually rare) in a specified space or time interval - Properties: a) Possible to partition a specified time or space interval into many smaller nonoverlapping subinterval b) # of outcomes in one subinterval is independent of another c) The probability that a single outcome will occur in a very short subinterval is proportional to the length of the subinterval d) The probability that more than 1 outcome will occur in such a shirt subinterval is almost đ?œ™ - đ?‘Ľ âˆź đ?‘ƒ0 (â‹‹)
-
pmf: đ?‘ƒđ?‘Ľ (đ?‘Ľ) =
-
đ??¸(đ?‘Ľ) =â‹‹
;
đ?‘’ −⋋⋋đ?‘Ľ đ?‘Ľ!
đ??ź[đ?‘œ,1,2,...} (đ?‘Ľ) ;
â‹‹> 0
đ?‘Łđ?‘Žđ?‘&#x;(đ?‘Ľ) =â‹‹
3. Binomial Distribution - F -> fixed # of n trials, đ?‘› > 1 - I -> independence - T ->two possible outcomes (success or failure) - S -> same probability of a success for each observation
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đ?‘Ľ âˆź đ??ľđ?‘– (đ?‘›1 đ?‘ƒ)
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pmf: đ?‘ƒđ?‘Ľ (đ?‘Ľ) = ( ) đ?‘ƒ đ?‘Ľ (1 − đ?‘ƒ)đ?‘›âˆ’đ?‘Ľ đ??ź{0,1,2,...,đ?‘›} đ?‘Ľ ; 0 ≤ đ?‘ƒ ≤ 1;
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đ??¸(đ?‘Ľ) = đ?‘›đ?‘?;
đ?‘› đ?‘Ľ đ?‘Łđ?‘Žđ?‘&#x;(đ?‘Ľ) = đ?‘›đ?‘?đ?‘ž -> đ?‘ž = 1 − đ?‘?
1
SRSWR
đ?‘› ∈ đ?‘§+