Probability Distribution – Example #2 - homework

Slides:

Advertisements

Similar presentations

The Normal Distribution

Advertisements

E(X 2 ) = Var (X) = E(X 2 ) – [E(X)] 2 E(X) = The Mean and Variance of a Continuous Random Variable In order to calculate the mean or expected value of.

Random Variables A random variable is a variable (usually we use x), that has a single numerical value, determined by chance, for each outcome of a procedure.

Unit 18 Section 18C The Binomial Distribution. Example 1: If a coin is tossed 3 times, what is the probability of obtaining exactly 2 heads Solution:

S2 Revision Quiz Answers coming up…. Question 1 (3 points) A string AB of length 5 cm is cut, in a random place C, into two pieces. The random variable.

Chapter 5 Probability Distributions

DISCRETE RANDOM VARIABLES. RANDOM VARIABLES numericalA random variable assigns a numerical value to each simple event in the sample space Its value is.

Equation: Mean Example data: DBH (in)CountSum SUM84656 Mean = 7.81.

Mutually Exclusive: P(not A) = 1- P(A) Complement Rule: P(A and B) = 0 P(A or B) = P(A) + P(B) - P(A and B) General Addition Rule: Conditional Probability:

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

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

Odds. 1. The odds in favor of an event E occurring is the ratio: p(E) / p(E C ) ; provided p(E C ) in not 0 Notations: The odds is, often, expressed in.

The Binomial Distribution

Examples for the midterm. data = {4,3,6,3,9,6,3,2,6,9} Example 1 Mode = Median = Mean = Standard deviation = Variance = Z scores =

GrowingKnowing.com © Expected value Expected value is a weighted mean Example You put your data in categories by product You build a frequency.

1 Chapter 16 Random Variables. 2 Expected Value: Center A random variable assumes a value based on the outcome of a random event.  We use a capital letter,

Chapter 5 Discrete Probability Distributions

22/10/2015 How many words can you make? Three or more letters Must all include A A P I Y M L F.

X = 2*Bin(300,1/2) – 300 E[X] = 0 Y = 2*Bin(30,1/2) – 30 E[Y] = 0.

Probability & Statistics I IE 254 Summer 1999 Chapter 4  Continuous Random Variables  What is the difference between a discrete & a continuous R.V.?

Mean and Standard Deviation of Discrete Random Variables.

7.3 and 7.4 Extra Practice Quiz: TOMORROW THIS REVIEW IS ON MY TEACHER WEB PAGE!!!

DATA MANAGEMENT MBF3C Lesson #5: Measures of Spread.

3.3 Working with Grouped Data Objectives: By the end of this section, I will be able to… 1) Calculate the weighted mean. 2) Estimate the mean for grouped.

Term 2 Week 3 Warm Ups. Warm Up 10/27/14 1.For each polynomial, determine which of the five methods of factoring you should use (GCF, trinomial, A≠1 trinomial,

The Median of a Continuous Distribution

Chapter 5 Discrete Probability Distributions. Random Variable A numerical description of the result of an experiment.

Normal Distribution. Normal Distribution: Symmetric: Mean = Median = Mode.

DISCRETE RANDOM VARIABLES.

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

7 sum of RVs. 7-1: variance of Z Find the variance of Z = X+Y by using Var(X), Var(Y), and Cov(X,Y)

By the end of this lesson you will be able to explain/calculate the following: 1. Mean for data in frequency table 2. Mode for data in frequency table.

Statistics 1: Introduction to Probability and Statistics Section 3-2.

Probability Distributions

Chapter 18 The Lognormal Distribution. Copyright © 2006 Pearson Addison-Wesley. All rights reserved The Normal Distribution Normal distribution.

1). Standard Deviation Normal Curve Standard Deviation mean.

12.6 – Probability Distributions. Properties of Probability Distributions.

WHAT IS STANDARD DEVIATION? MONA BEHROUZIAN MATH 10H.

Section 5.2: PROBABILITY AND THE NORMAL DISTRIBUTION.

Example Suppose that we take a random sample of eight fuel efficient cars and record the gas mileage. Calculate the following for the results: 33, 41,

The Variance of a Random Variable Lecture 35 Section Fri, Mar 26, 2004.

Ex St 801 Statistical Methods Inference about a Single Population Mean (CI)

Normal Probability Distributions Chapter 5. § 5.2 Normal Distributions: Finding Probabilities.

7.2 Means & Variances of Random Variables AP Statistics.

Mean, Median, and Mode Lesson 7-1. Mean The mean of a set of data is the average. Add up all of the data. Divide the sum by the number of data items you.

Chapter 7 Lesson 7.4a Random Variables and Probability Distributions 7.4: Mean and Standard Deviation of a Random Variable.

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

Discrete Probability Distributions

Umm Al-Qura University

Random Variable 2013.

DISCRETE RANDOM VARIABLES

Random Variables and Probability Distribution (2)

Homework #3 Solution Write the distribution for formula and determine whether it is a probability distribution or not if it is then calculated mean, variance.

Measures of Central Tendency

Discrete Probability Distributions

Means and Variances of Random Variables

Notes Over 7.7 Finding Measures of Central Tendency

CONTINUOUS PROBABILITY DISTRIBUTIONS CHAPTER 15

Stem & Leaf Plots How to make a Stem & Leaf Plot.

Probability Review for Financial Engineers

Mean & Variance for the Binomial Distribution

Statistics 1: Introduction to Probability and Statistics

Exam 2 - Review Chapters

10-5 The normal distribution

Ch. 6. Binomial Theory.

Calculating probabilities for a normal distribution

Stem & Leaf Plots How to make a Stem & Leaf Plot.

Presentation transcript:

Probability Distribution – Example #2 - homework Calculate the Mean, Median, Mode, Variance and Standard Deviation of the following probability distribution:

Example #2 - Homework X (unsorted) p(X) X (sorted) 7 0.4 2 0.1 4 0.3 8 0.2 Sum 1.0

Example #2 Mean = E(X) = Expected Value = 2(.1) + 4(.3) + 7(.4) + 8(.2) = 5.8; Median = 7; Mode = 7 [p(X) = 0.4]; 1) E(X2) = 22  0.1 + 42  0.3 + 72  0.4 + 82  0.2 = 37.6; 2) [E(X)]2 = 5.82 = 33.64;

Example #2 – Cont’d VAR(X) = E(X2) – [E(X)]2  37.6 – 33.64 = 3.96;  = 3.96 = 1.99.