Continuous Random Variable (1)

Continuous Random Variable (1) Section 3.1-3.3

Upload
blaine-maxwell
Category

Documents
view
44
download
0

Embed Size (px):

description

Continuous Random Variable (1). Section 3.1-3.3. Continuous Random Variable. What is the probability that X is equal to x ?. CDF for a Discrete Random Variables. Question: Is there a CDF for a continuous random variable if a PMF can not be identified for a continuous random variable?. - PowerPoint PPT Presentation

Transcript of Continuous Random Variable (1)

Continuous Random Variable (1)

Section 3.1-3.3

Continuous Random Variable

What is the probability that X is equal to x?

CDF for a Discrete Random Variables

Question: Is there a CDF for a continuous random variable if a PMF can not beidentified for a continuous random variable?

CDF for a Wheel-Spinning Experiment

P[X=≤ x]=x if 0 ≤X ≤1

CDF for Continuous Random Variable

• Even though it is not possible to define a PDF for a continuous random variable, it is possible to define a CDF for a random variable

PMF to CDF for a Discrete Random Variable

Theorem 2.2

Theorem 2.3

What contributes to the jump in the CDF?

Discrete RV

Continuous RV

Compare CDF of a Continuous RV to that of a Discrete RV

Discrete RV:1. Zero slope2. Jumps in CDF

Continuous RV:A continuous function

Slope of CDF function

The slope at any point x indicates the probability that X is near x.

(Just as the jump in the CDF of a discrete RV suggests non-zero probability at X=x, so does a slope in CDF of a continuous random variable?)

Probability Density Function (PDF)

It is not possible to define a PMF function for a continuous variable because P[X=x]=0.We can, however, define a probability density function.

Properties of fX(x)

PDF of X

Expected Value

Discrete Random Variable

Continuous Random Variable

7.1 – Discrete and Continuous Random Variables. Random Variable: A variable whose value is a numerical outcome of a random phenomenon Discrete Random.

7. continuous random variables - courses.cs.washington.edu · 2017. 10. 15. · continuous random variables Discrete random variable: values in a ﬁnite or countable set, e.g. X

Random variable – Discrete Probability distribution ... II Y… · A random variable X has the following ... For a continuous random variable X which ... The variance of a Random

Continuous Probability Distributions Continuous Random Variable A random variable whose space (set of possible values) is an entire interval of numbers.

Topic 7: Random Variables and Distribution Functionsjwatkins/g-randomvariables.pdf · board random variable. So, distribution functions for continuous random random vari-ables increase

Section 6.2: Generating Discrete Random Variates...Random Variate Generation By Inversion X is a discrete random variable with idf F∗(·) Continuous random variable U is Uniform(0,1)

CURRICULUM PACING GUIDE - Collier County Public ... · Web viewDiscrete random variable, continuous random variable, population parameters, mean µ of a probability distribution, standard

ACADEMIC ACTION PLAN FOR 2nd YEAR€¦ · Random variable : Discrete and continuous distribution of a random variable, p.m.f. and p.d.f., Distribution function. 2.7. Mathematical

Chapter 4: Continuous Random Variable 4...Continuous Random Variable Cont’d I Because the number of possible values of X is uncountably in nite, the probability mass function (pmf)

Random Variable and Probability Distribution. 2 Outline of Lecture Random Variable –Discrete Random Variable. –Continuous Random Variables. Probability.

Chapter 4 Continuous Random Variables - Purdue University · Chapter 4 Continuous Random Variables A random variable can be discrete, continuous, or a mix of both. Discrete random

Chapter 5bkrein/Introductory Statistics... · A Discrete Random Variable is a random variable that can only take on a countable number of possible values. A Continuous Random Variable

1 Continuous random variables f(x) x. 2 Continuous random variables A discrete random variable has values that are isolated numbers, e.g.: Number of boys.

1 Continuous random variables Continuous random variable Let X be such a random variable Takes on values in the real space (-infinity; +infinity) (lower.

18.440: Lecture 17 .1in Continuous random variablesmath.mit.edu/~sheffield/440/Lecture17.pdf · 18.440 Lecture 17. Continuous random variables I Say X is a continuous random variable

Random Variable Qualitative (categorical) Quantitative (numeric) NominalOrdinal Ratio Interval Continuous Discrete.

Section 7.2: Generating Continuous Random Variates...Random Variate Generation By Inversion X is a continuous random variable with idf F−1(·) Continuous random variable U is Uniform(0,1)

$Basic Concepts Random Variables { discrete random …kosorok/bios760sub/ChapA_Slide+Note.pdf · { discrete random variable: probability mass function { continuous random variable:$

Basic Concepts Random Variables { discrete random …kosorok/bios760sub/ChapA_Slide+Note.pdf · { discrete random variable: probability mass function { continuous random variable:

Continuous Random Variables - WebAssign... The values of discrete and continuous random variables can be ... you drive to work, then X is a discrete random variable. ... Probability

Continuous Random Variable (1)

Documents

Transcript of Continuous Random Variable (1)