6.2/6.3 Probability Distributions and Distribution Mean

Slides:

Advertisements

Similar presentations

Let X 1, X 2,..., X n be a set of independent random variables having a common distribution, and let E[ X i ] = . then, with probability 1 Strong law.

Advertisements

Review of Probability. Definitions (1) Quiz 1.Let’s say I have a random variable X for a coin, with event space {H, T}. If the probability P(X=H) is.

Chapter 12 Probability © 2008 Pearson Addison-Wesley. All rights reserved.

Excursions in Modern Mathematics, 7e: Copyright © 2010 Pearson Education, Inc. 16 Mathematics of Managing Risks Weighted Average Expected Value.

Random Variables.

Section 7.4 (partially). Section Summary Expected Value Linearity of Expectations Independent Random Variables.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 4-1 Introduction to Statistics Chapter 5 Random Variables.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Discrete random variables Probability mass function Distribution function (Secs )

Statistics Lecture 8. Last day/Today: Discrete probability distributions Assignment 3: Chapter 2: 44, 50, 60, 68, 74, 86, 110.

Random Variables November 23, Discrete Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon.

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.

Expected Value.  In gambling on an uncertain future, knowing the odds is only part of the story!  Example: I flip a fair coin. If it lands HEADS, you.

Probability Distributions: Finite Random Variables.

Quiz 4  Probability Distributions. 1. In families of three children what is the mean number of girls (assuming P(girl)=0.500)? a) 1 b) 1.5 c) 2 d) 2.5.

Mean, Variance, and Standard Deviation

P(Y≤ 0.4) P(Y < 0.4) P(0.1 < Y ≤ 0.15)

Probability and Statistics Dr. Saeid Moloudzadeh Axioms of Probability/ Basic Theorems 1 Contents Descriptive Statistics Axioms of Probability.

Sets, Combinatorics, Probability, and Number Theory Mathematical Structures for Computer Science Chapter 3 Copyright © 2006 W.H. Freeman & Co.MSCS SlidesProbability.

Sets, Combinatorics, Probability, and Number Theory Mathematical Structures for Computer Science Chapter 3 Copyright © 2006 W.H. Freeman & Co.MSCS SlidesProbability.

The Binomial Distribution Permutations: How many different pairs of two items are possible from these four letters: L, M. N, P. L,M L,N L,P M,L M,N M,P.

Binomial Distributions Calculating the Probability of Success.

Probability Distributions - Discrete Random Variables Outcomes and Events.

4.1 Probability Distributions. Do you remember? Relative Frequency Histogram.

Chapter 5.1 Probability Distributions.  A variable is defined as a characteristic or attribute that can assume different values.  Recall that a variable.

Random Variables. A random variable X is a real valued function defined on the sample space, X : S  R. The set { s  S : X ( s )  [ a, b ] is an event}.

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 Binomial Experiments Section 4-3 & Section 4-4 M A R I O F. T R I O L A Copyright.

Binomial Experiment A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties:

Chapter 5: The Binomial Probability Distribution and Related Topics Section 1: Introduction to Random Variables and Probability Distributions.

Math b (Discrete) Random Variables, Binomial Distribution.

4.1 Probability Distributions NOTES Coach Bridges.

4.1 Probability Distributions Important Concepts –Random Variables –Probability Distribution –Mean (or Expected Value) of a Random Variable –Variance and.

Chapter 7 Random Variables. Usually notated by capital letters near the end of the alphabet, such as X or Y. As we progress from general rules of probability.

Warm Up Section Explain why the following is not a valid probability distribution? 2.Is the variable x discrete or continuous? Explain. 3.Find the.

12/24/ Probability Distributions. 12/24/ Probability Distributions Random Variable – a variable whose values are numbers determined.

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

Section 7.1 Discrete and Continuous Random Variables

Review Know properties of Random Variables

Chapter 4 Discrete Probability Distributions 4.1 Probability Distributions I.Random Variables A random variable x represents a numerical value associated5with.

MATH 2311 Section 3.2. Bernoulli Trials A Bernoulli Trial is a random experiment with the following features: 1.The outcome can be classified as either.

Random Variables If  is an outcome space with a probability measure and X is a real-valued function defined over the elements of , then X is a random.

Probability Distribution. Probability Distributions: Overview To understand probability distributions, it is important to understand variables and random.

Discrete and Continuous Random Variables Section 7.1.

Mean, variance, standard deviation and expectation

Unit 5 Section 5-2.

Random Variables and Probability Distribution (2)

The Binomial and Geometric Distributions

MATH 2311 Section 3.2.

Section 8.4 – Continuous Probability Models

Distributions and expected value

Review for test Ch. 6 ON TUESDAY:

7.5 The Normal Curve Approximation to the Binomial Distribution

Discrete Distributions

Discrete Distributions

Continuous Random Variable Normal Distribution

If you are interested in participating in Math Competitions beyond GMLT, send Coach Hoffa your school address. sure.

Ch. 6. Binomial Theory.

MATH 2311 Section 3.2.

Discrete Distributions.

Section 7.1 Discrete and Continuous Random Variables

Tutorial 7 Probability and Calculus

Discrete Distributions

6: Binomial Probability Distributions

Lesson #5: Probability Distributions

Standard Deviation for Probability Distributions

QUIZ #1 30 minutes.

CSE 321 Discrete Structures

IE 360: Design and Control of Industrial Systems I

MATH 2311 Section 3.2.

Chapter 11 Probability.

Presentation transcript:

6.2/6.3 Probability Distributions and Distribution Mean Advanced Math Topics 6.2/6.3 Probability Distributions and Distribution Mean

A discrete random variable. # of Assignments Turned in (x) A continuous random variable would have decimal values. Probability 1/19 1 2/19 2 4/19 3 5/19 4 7/19 19/19 = 1 The probability total will always be 1. This is an example of a probability distribution.

Create a probability distribution for the random variable of x, the number of heads on three coin flips. # of Heads (x) Probability 1/8 1 3/8 H H H H H T H T H 2 3/8 H T T T T T 3 1/8 T T H T H T 8/8 = 1 T H H

μ = Σ x • p(x) To find the mean of the probability distribution: Find the mean of the probability distribution from the last slide. # of Heads (x) Probability x • p(x) 1/8 1 3/8 3/8 2 3/8 6/8 3 1/8 3/8 μ = 12/8 = 1.5

From the HW P. 294 10) A farmer plants four seedlings. Let x be the number of seedlings that sprout. Find the probability distribution of x. Assume that a seedling dying or sprouting has equal probability. # of Heads (x) Probability 1/16 1 4/16 2 6/16 3 4/16 4 1/16 16/16 = 1

From the HW P. 306 1) Find the mean of the distribution. # of Mail Pieces (x) Probability x • p(x) 0.02 1 0.03 0.03 2 0.25 0.5 3 0.19 0.57 4 0.16 0.64 5 0.14 0.70 6 0.12 0.72 7 0.08 0.56 8 0.01 0.08 μ = 3.8

HW P. 295 #1-7, 10 , 11, 16 P. 306 Compute the mean only for #1-4