A Simple Random Variable, A Fair D6 and the Inheritance of Probabilities through Random Variables.

Slides:

Advertisements

Similar presentations

Designing Investigations to Predict Probabilities Of Events.

Advertisements

Probability COMPOUND EVENTS. If two sets or events have no elements in common, they are called disjoint or mutually exclusive. Examples of mutually exclusive.

Rare Events, Probability and Sample Size. Rare Events An event E is rare if its probability is very small, that is, if Pr{E} ≈ 0. Rare events require.

16.1 Approximate Normal Approximately Normal Distribution: Almost a bell shape curve. Normal Distribution: Bell shape curve. All perfect bell shape curves.

Week11 Parameter, Statistic and Random Samples A parameter is a number that describes the population. It is a fixed number, but in practice we do not know.

Sampling: Final and Initial Sample Size Determination

Who Wants To Be A Millionaire?

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

Mathematics in Today's World

1. (f) Use continuity corrections for discrete random variable LEARNING OUTCOMES At the end of the lesson, students will be able to (g) Use the normal.

Histogram Specification

Games of probability What are my chances?. Roll a single die (6 faces). –What is the probability of each number showing on top? Activity 1: Simple probability:

Random Variables.

Slide 5-2 Copyright © 2008 Pearson Education, Inc. Chapter 5 Probability and Random Variables.

Three Dice - An Exploration of Conditional Probability.

PROBABILITY  A fair six-sided die is rolled. What is the probability that the result is even?

Chapter 6 Section 1 Introduction. Probability of an Event The probability of an event is a number that expresses the long run likelihood that an event.

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

Section 1.2 Suppose A 1, A 2,..., A k, are k events. The k events are called mutually exclusive if The k events are called mutually exhaustive if A i 

2003/02/13 Chapter 4 1頁1頁 Chapter 4 : Multiple Random Variables 4.1 Vector Random Variables.

Chapter 7 Expectation 7.1 Mathematical expectation.

UNR, MATH/STAT 352, Spring Head Tail Tossing a symmetric coin You are paying $1 How much should you get to make the game fair?

1 Random numbers Random  completely unpredictable. No way to determine in advance what value will be chosen from a set of equally probable elements. Impossible.

Discrete and Continuous Random Variables Continuous random variable: A variable whose values are not restricted – The Normal Distribution Discrete.

The Central Limit Theorem For simple random samples from any population with finite mean and variance, as n becomes increasingly large, the sampling distribution.

Lottery Problem A state run monthly lottery can sell 100,000tickets at $2 a piece. A ticket wins $1,000,000with a probability , $100 with probability.

Chapter 7 Random Variables I can find the probability of a discrete random variable. 6.1a Discrete and Continuous Random Variables and Expected Value h.w:

Raymond Martin Lecture 7 – Sampling Data are collected to represent a population or study area. –A census is complete enumeration.

Normal Approximation Of The Binomial Distribution:

Binomial Distributions Calculating the Probability of Success.

Poisson Random Variable Provides model for data that represent the number of occurrences of a specified event in a given unit of time X represents the.

Simple Mathematical Facts for Lecture 1. Conditional Probabilities Given an event has occurred, the conditional probability that another event occurs.

Probability (Grade 12) Daljit Dhaliwal. Sticks and Stones game.

14/6/1435 lecture 10 Lecture 9. The probability distribution for the discrete variable Satify the following conditions P(x)>= 0 for all x.

Delivering Integrated, Sustainable, Water Resources Solutions Monte Carlo Simulation Robert C. Patev North Atlantic Division – Regional Technical Specialist.

Expected Value. Expected Value - Definition The mean (average) of a random variable.

Chapter 7 Sampling and Sampling Distributions ©. Simple Random Sample simple random sample Suppose that we want to select a sample of n objects from a.

Continuous Random Variables Lecture 25 Section Mon, Feb 28, 2005.

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

By Satyadhar Joshi. Content  Probability Spaces  Bernoulli's Trial  Random Variables a. Expectation variance and standard deviation b. The Normal Distribution.

Probability Distributions, Discrete Random Variables

1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean.

© 2010 Pearson Prentice Hall. All rights reserved Chapter Sampling Distributions 8.

The Mean of a Discrete Random Variable Lesson

Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:

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

Learning Objectives 1. Understand how the Small Basic Turtle operates. 2. Be able to draw geometric patterns using iteration.

Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. B ASIC C ONCEPTS IN P ROBABILITY Section 5.1.

Random Variables and Probability Distributions. Definition A random variable is a real-valued function whose domain is the sample space for some experiment.

Continuous Random Variables

Reading a Normal Curve Table

Chapter 5 Review MDM 4U Mr. Lieff.

Chapter 5 Review MDM 4U Gary Greer.

Hire Toyota Innova in Delhi for Outstation Tour

SA3202 Statistical Methods for Social Sciences

اختر أي شخصية واجعلها تطير!

The Normal Approximation to the Binomial Distribution

Sampling Distribution Models

Reconstructing a Function from its Gradient

Distributions and expected value

Section 1.1: Equally Likely Outcomes

مديريت موثر جلسات Running a Meeting that Works

Continuous Random Variables

Continuous Random Variable Normal Distribution

e is the possible out comes for a model

Review of Hypothesis Testing

Discrete Random Variables: Basics

Uniform Probability Distribution

Chapter 11 Probability.

Presentation transcript:

A Simple Random Variable, A Fair D6 and the Inheritance of Probabilities through Random Variables

The Fair d6 Model Face Values: 1,2,3,4,5,6 Fair Model: Equally likely face values – 1/6 per face value Pr{d6 Shows 1} = or 16.67% In long runs of tosses, approximately 1 toss in 6 shows “1”. Pr{d6 Shows 2} = or 16.67% In long runs of tosses, approximately 1 toss in 6 shows “2”. Pr{d6 Shows 3} = or 16.67% In long runs of tosses, approximately 1 toss in 6 shows “3”. Pr{d6 Shows 4} = or 16.67% In long runs of tosses, approximately 1 toss in 6 shows “4”. Pr{d6 Shows 5} = or 16.67% In long runs of tosses, approximately 1 toss in 6 shows “5”. Pr{d6 Shows 6} = or 16.67% In long runs of tosses, approximately 1 toss in 6 shows “6”.

Map D6 to D3 and Note D3 Face Value D6 Face Value  D3 Face Value 1, 2  1 3, 4  2 5, 6  3 This is a simple random variable.

The Fair d3 Model Nested within a Fair d6 Model FV: Face Values: 1(1,2), 2(3,4), 3(5,6) Fair Model: Equally likely face values – (2/6 =)1/3 per face value. Pr{d3 shows “1”} = Pr{d6 Shows 1} + Pr{d6 Shows 2} = (1/6) + (1/6) = 2/6 = 1/3 In long runs of tosses, approximately 1 toss in 3 shows “1”. Pr{d3 shows “2”} = Pr{d6 Shows 3} + Pr{d6 Shows 4} = (1/6) + (1/6) = 2/6 = 1/3 In long runs of tosses, approximately 1 toss in 3 shows “2”. Pr{d3 shows “3”} = Pr{d6 Shows 5} + Pr{d6 Shows 6} = (1/6) + (1/6) = 2/6 = 1/3 In long runs of tosses, approximately 1 toss in 3 shows “3”.