Warm-up 1. A concert hall has 2000 seats. There are 1200 seats on the main floor and 800 in the balcony. 40% of those in the balcony buy a souvenir program.

Slides:

Advertisements

Similar presentations

CHAPTER Discrete Models  G eneral distributions  C lassical: Binomial, Poisson, etc Continuous Models  G eneral distributions  C.

Advertisements

Chapter 6 Introduction to Continuous Probability Distributions

Today Today: Chapter 5 Reading: –Chapter 5 (not 5.12) –Suggested problems: 5.1, 5.2, 5.3, 5.15, 5.25, 5.33, 5.38, 5.47, 5.53, 5.62.

Lesson #15 The Normal Distribution. For a truly continuous random variable, P(X = c) = 0 for any value, c. Thus, we define probabilities only on intervals.

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.

CONTINUOUS RANDOM VARIABLES. Continuous random variables have values in a “continuum” of real numbers Examples -- X = How far you will hit a golf ball.

Probability Distributions Random Variables: Finite and Continuous Distribution Functions Expected value April 3 – 10, 2003.

1 The Uniform Probability Distribution. 2 A rectangle The base of the rectangle The height of the rectangle Do you remember how to calculate the area.

Chapter 6: Some Continuous Probability Distributions:

Probability Distributions Continuous Random Variables.

Normal distribution and introduction to continuous random variables and continuous probability density functions...

Continuous Probability Distributions

Chapter 5: Continuous Random Variables

LECTURE UNIT 4.3 Normal Random Variables and Normal Probability Distributions.

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

Introduction to Normal Distributions and the Standard Distribution

© 2010 Pearson Education Inc.Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS, 12e – Slide 1 of 15 Chapter 12 Probability and Calculus.

L7.1b Continuous Random Variables CONTINUOUS RANDOM VARIABLES NORMAL DISTRIBUTIONS AD PROBABILITY DISTRIBUTIONS.

Chapter 6 The Normal Probability Distribution

Starter The probability distribution of a discrete random variable X is given by: P(X = r) = 30kr for r = 3, 5, 7 P(X = r) = 0 otherwise What is the value.

Continuous Random Variables and Probability Distributions

Lesson 7 - R Review of Random Variables. Objectives Define what is meant by a random variable Define a discrete random variable Define a continuous random.

QBM117 Business Statistics Probability and Probability Distributions Continuous Probability Distributions 1.

Continuous Distributions. The distributions that we have looked at so far have involved DISCRETE Data The distributions that we have looked at so far.

Normal distribution and intro to continuous probability density functions...

Chapter 6 Normal Probability Distribution Lecture 1 Sections: 6.1 – 6.2.

Modular 11 Ch 7.1 to 7.2 Part I. Ch 7.1 Uniform and Normal Distribution Recall: Discrete random variable probability distribution For a continued random.

Chapter 7 Lesson 7.3 Random Variables and Probability Distributions 7.3 Probability Distributions for Continuous Random Variables.

The Median of a Continuous Distribution

Discrete and Continuous Variables

MATH 4030 – 4B CONTINUOUS RANDOM VARIABLES Density Function PDF and CDF Mean and Variance Uniform Distribution Normal Distribution.

© 2010 Pearson Prentice Hall. All rights reserved Chapter The Normal Probability Distribution © 2010 Pearson Prentice Hall. All rights reserved 3 7.

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

Continuous Random Variables Section Starter A 9-sided die has three faces that show 1, two faces that show 2, and one face each showing 3,

CONTINUOUS RANDOM VARIABLES

Discrete and Continuous Random Variables. Yesterday we calculated the mean number of goals for a randomly selected team in a randomly selected game.

Chapter 5 CONTINUOUS RANDOM VARIABLES

AP STATISTICS Section 7.1 Random Variables. Objective: To be able to recognize discrete and continuous random variables and calculate probabilities using.

1 7.5 CONTINUOUS RANDOM VARIABLES Continuous data occur when the variable of interest can take on anyone of an infinite number of values over some interval.

Chapter 4 Continuous Random Variables and Probability Distributions

2.Find the turning point of the function given in question 1.

1 1 Slide Continuous Probability Distributions n The Uniform Distribution  a b   n The Normal Distribution n The Exponential Distribution.

Density Curves. Weight of newborns Nearest pound Nearest tenth of pound

Lesson Applications of the Normal Distribution.

11.3 CONTINUOUS RANDOM VARIABLES. Objectives: (a) Understand probability density functions (b) Solve problems related to probability density function.

Chapter 7 Random Variables and Continuous Distributions.

4.3 Probability Distributions of Continuous Random Variables: For any continuous r. v. X, there exists a function f(x), called the density function of.

SWBAT: -Distinguish between discrete and continuous random variables -Construct a probability distribution and its graph -Determine if a distribution is.

4-1 Continuous Random Variables 4-2 Probability Distributions and Probability Density Functions Figure 4-1 Density function of a loading on a long,

Continuous Probability Distribution

Transforming Data.

Section 7.3: Probability Distributions for Continuous Random Variables

4.3 Probability Distributions of Continuous Random Variables:

Properties of the Normal Distribution

Continuous random variables and probability distributions

Continuous Random Variables

CONTINUOUS RANDOM VARIABLES

Exponential Probabilities

Continuous Probability Distributions Part 2

4.3 Probability Distributions of Continuous Random Variables:

Continuous Random Variables

Histograms © T Madas.

10-5 The normal distribution

Continuous Probability Distributions Part 2

Lecture 12: Normal Distribution

Uniform Distribution Is a continuous distribution that is evenly (or uniformly) distributed Has a density curve in the shape of a rectangle Probabilities.

Continuous Random Variables

Uniform Probability Distribution

Normal Probability Distribution Lecture 1 Sections: 6.1 – 6.2

Presentation transcript:

Warm-up 1. A concert hall has 2000 seats. There are 1200 seats on the main floor and 800 in the balcony. 40% of those in the balcony buy a souvenir program. 50% of those on the main floor buy a souvenir program. At a certain performance all seats are occupied. If an audience member is selected at random, what is the probability that a program was purchased? 2. A spinner on a full circle can take on any decimal value between 0 and 400. What is the probability that the spinner will land between 175 and 225?

Continuous Random Variables Density Functions

Continuous Random Variables Possible values contain an entire interval.

Ex: Weight of newborns Nearest pound Nearest tenth of pound

Fit more & more rectangles It approaches a curve as the rectangles become smaller & has greater accuracy.

Density Function Probability distribution for a continuous random variable (f(x)). The graph is a smooth curve called the density curve. F(x)  0 Total area under the curve = 1.

Uniform Distribution All occur in equal distributions

Ex: What’s the area from 4.5 to 5.5?What’s the area from 5.5 to 6?

Discrete:

Continuous: Why? It’s like finding the area of a rectangle with width = 0.

Probabilities for continuous random variables are usually calculated using cumulative areas. P(x<0.5) Found using integrals & calculus – but we’ll use tables!

If we have a uniform continuous function from 3 to 8, find the height.

Ex. Find P(x < 10) Find P(x < 35) minutes

Ex: Find P(x<4) Find P(x<2) 0.25

Ex: Find P(x<20) Find P(x>70) Find P(20<x<70)

Homework P. 365 (20-26)