Stat 130 chapter 3

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Stat 130 – Intro to Math Stat for CS Chapter 3 Reviewer

Random Variable - A function from Ί into the set ___ of real #s - A function whose value is a real number - Domain: Ί - Counter domain: ____ - X (random var.) Ί - X (elements of the range)

Cumulative Distribution Function (CDF) -> đ??šđ?‘Ľ (.) - Function defined for any ____ x as đ??šđ?‘Ľ (đ?‘Ľ) = đ?‘ƒ(đ?‘‹ ≤ đ?‘Ľ) - Possibility ___ [0, 1] - Non-decreasing ___ - Every RV will have one & any one CDF - If đ??šđ?‘Ľ (.) is the cdf of a RV X, then for any _____ a and b, đ?‘Ž < đ?‘?: 1) đ?‘ƒ(đ?‘Ž < đ?‘‹ ≤ đ?‘?) = đ??šđ?‘Ľ (đ?‘?) − đ??šđ?‘Ľ (đ?‘Ž) 2) đ?‘ƒ(đ?‘‹ < đ?‘Ž) = ____ − đ??šđ?‘Ľ (đ?‘Ľ) = đ??šđ?‘Ľ (đ?‘Žâˆ’ ) 3) đ?‘ƒ(đ?‘Ž ≤ đ?‘‹ ≤ đ?‘?) = đ??šđ?‘Ľ (đ?‘?) − đ??šđ?‘Ľ (đ?‘Žâˆ’ ) 4) đ?‘ƒ(đ?‘Ž ≤ đ?‘‹ < đ?‘?) = đ??šđ?‘Ľ (đ?‘?− ) − đ??šđ?‘Ľ (đ?‘Žâˆ’ ) 5) đ?‘ƒ(đ?‘Ž < đ?‘‹ < đ?‘?) = đ??šđ?‘Ľ (đ?‘?− ) − đ??šđ?‘Ľ (đ?‘Ž) 6) đ?‘ƒ(đ?‘‹ > đ?‘Ž) = 1 − đ??šđ?‘Ľ (đ?‘Ž) 7) đ?‘ƒ(đ?‘‹ ≼ đ?‘Ž) = 1 − đ??šđ?‘Ľ (đ?‘Žâˆ’ ) 8) đ?‘ƒ(đ?‘‹ = đ?‘Ž) = đ??šđ?‘Ľ (đ?‘Ž) − đ??šđ?‘Ľ (đ?‘Žâˆ’ ) -> if continuous, then = 0 - Any function with domain = ______ counter domain = [0,1] that statistics the ff. is a CDF: 1) đ??šđ?‘Ľ (−âˆ?) = _____ đ??šđ?‘Ľ (đ?‘‹) = 0 and đ??šđ?‘Ľ (âˆ?) = ______ đ??šđ?‘Ľ (đ?‘‹) = 1 2) đ??šđ?‘Ľ (. ) is a monotone, nondecreasing function ( đ??šđ?‘Ľ (đ?‘Ž) ≤ đ??šđ?‘Ľ (đ?‘?)đ?‘“đ?‘œđ?‘&#x; đ?‘Žđ?‘›đ?‘˘ đ?‘Ž < đ?‘?) 3) đ??šđ?‘Ľ (. ) is a continuous from the right ( ______ đ??šđ?‘Ľ (đ?‘Ľ + â„Ž) = đ??šđ?‘Ľ (đ?‘‹) for all x )

Discrete Random Variables ďƒ˜ Sample space contains a finite # of sample points -> Discrete sample space ďƒ˜ RV defined over a discrete sample space

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Stat 130 chapter 3 by UP CURSOR Library - Issuu