{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}


exampleclass3solution - THE UNIVERSITY OF HONG KONG...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 PROBABILITY AND STATISTICS I, FALL 2010 EXAMPLE CLASS 3 Random Variable Elements of Theory A function (with some requirement) defined on the sample space { } is called a random variable. - Domain is the sample space - Range is usually a numbers set, e.g., or its subsets, for easy manipulation. - The range is called the state space of the random variable. There is no intrinsic difference on the nature between a sample space and a state space they are just two sets with some requirement, called “measurability.” They are just domain and range of a “function” with some requireme nt, called “measurability.” The variable perspective is adopted by an observer of a random experiment. The observer is only able to observe/know/measure/obtain information based on the state space. For the observer, all she could see is a variable dancing (randomly) on the state space. This is the perspective that we will primarily study in this course. The function perspective is adopted by someone who would have a “divine” capacity in understanding (a deterministic part of) the design of the random mechanism, in particular, her capacity in seeing the existence of an
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
underlying sample space as the domain of a function sending elements of the domain to the state space. You will be studying this perspective in an advanced course of probability. There is a law governing how any random variable to be observed in its state space. The law is a probabilistic one, called the probability distribution of a random variable. There are two qualifications for any real-valued function to be a probability density/mass function, aka, probability function: 1) for any , 2) or .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 7

exampleclass3solution - THE UNIVERSITY OF HONG KONG...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online