Practice Problems Actex 3, 4, 5. Section 3 -- #3 A box contains 4 red balls and 6 white balls. A sample of size 3 is drawn without replacement from the.

Slides:

Advertisements

Similar presentations

McGraw-Hill/Irwin Copyright © 2004 by the McGraw-Hill Companies, Inc. All rights reserved. Chapter 3 Risk Identification and Measurement.

Advertisements

Ka-fu Wong © 2003 Chap 8- 1 Dr. Ka-fu Wong ECON1003 Analysis of Economic Data.

Chapter 2 Discrete Random Variables

1 Discrete Probability Distributions. 2 Random Variable Random experiment is an experiment with random outcome. Random variable is a variable related.

Continuous Random Variables and Probability Distributions

Hypergeometric Random Variables. Sampling without replacement When sampling with replacement, each trial remains independent. For example,… If balls are.

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

Random Variable (RV) A function that assigns a numerical value to each outcome of an experiment. Notation: X, Y, Z, etc Observed values: x, y, z, etc.

Problem 1 The following facts are known regarding two events A and B: Pr(A∩B) = 0.2,Pr(AUB) = 0.6,Pr(A | B) = 0.5 Find the following: (i)Pr (A) (ii)Pr.

QBM117 Business Statistics

BCOR 1020 Business Statistics

Statistics and Probability Theory Prof. Dr. Michael Havbro Faber

Section 09.  This table is on page 280 of the Actex manual Distribution of XiDistribution of Y Bernoulli B(1,p)Binomial B(k,p) Binomial.

5-3 Inference on the Means of Two Populations, Variances Unknown

NIPRL Chapter 2. Random Variables 2.1 Discrete Random Variables 2.2 Continuous Random Variables 2.3 The Expectation of a Random Variable 2.4 The Variance.

The Poisson Probability Distribution The Poisson probability distribution provides a good model for the probability distribution of the number of “rare.

This is a discrete distribution. Poisson is French for fish… It was named due to one of its uses. For example, if a fish tank had 260L of water and 13.

Chapter 7: The Normal Probability Distribution

CA200 Quantitative Analysis for Business Decisions.

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Chapter 5. Continuous Probability Distributions Sections 5.2, 5.3: Expected Value of Continuous Random.

Practice Problems Actex 8. Section 8 -- #5 Let T 1 be the time between a car accident and reporting a claim to the insurance company. Let T 2 be the time.

Copyright ©2011 Nelson Education Limited The Normal Probability Distribution CHAPTER 6.

1 Sampling Distributions Lecture 9. 2 Background  We want to learn about the feature of a population (parameter)  In many situations, it is impossible.

 A probability function is a function which assigns probabilities to the values of a random variable.  Individual probability values may be denoted by.

Probabilistic and Statistical Techniques 1 Lecture 19 Eng. Ismail Zakaria El Daour 2010.

 A probability function is a function which assigns probabilities to the values of a random variable.  Individual probability values may be denoted by.

Free Powerpoint Templates ROHANA BINTI ABDUL HAMID INSTITUT E FOR ENGINEERING MATHEMATICS (IMK) UNIVERSITI MALAYSIA PERLIS MADAM ROHANA BINTI ABDUL HAMID.

IE241 Problems. 1. Three fair coins are tossed in the air. What is the probability of getting 3 heads when they land?

HYPERGEOMETRIC DISTRIBUTION PREPARED BY :A.TUĞBA GÖRE

Sampling Distribution of the Sample Mean. Example a Let X denote the lifetime of a battery Suppose the distribution of battery battery lifetimes has 

Statistical Applications Binominal and Poisson’s Probability distributions E ( x ) =  =  xf ( x )

King Saud University Women Students

 A probability function is a function which assigns probabilities to the values of a random variable.  Individual probability values may be denoted.

Math b (Discrete) Random Variables, Binomial Distribution.

Machine Learning Chapter 5. Evaluating Hypotheses

Distributions.ppt - © Aki Taanila1 Discrete Probability Distributions.

Uniform Distributions and Random Variables Lecture 23 Sections 6.3.2, Mon, Oct 25, 2004.

Some Common Discrete Random Variables. Binomial Random Variables.

Chapter 4-5 DeGroot & Schervish. Conditional Expectation/Mean Let X and Y be random variables such that the mean of Y exists and is finite. The conditional.

Math 4030 – 6a Joint Distributions (Discrete)

 A probability function is a function which assigns probabilities to the values of a random variable.  Individual probability values may be denoted.

Chapter 4. Random Variables - 3

C HAPTER 4  Hypothesis Testing -Test for one and two means -Test for one and two proportions.

Section 6.4 Inferences for Variances. Chi-square probability densities.

Statistics Sampling Distributions and Point Estimation of Parameters Contents, figures, and exercises come from the textbook: Applied Statistics and Probability.

Practice Problems Actex Sections 6, 7. Section 6 -- #3 A company prices its hurricane insurance using the following assumptions: – In any calendar year,

Section 1.3 Each arrangement (ordering) of n distinguishable objects is called a permutation, and the number of permutations of n distinguishable objects.

Unit 4 Review. Starter Write the characteristics of the binomial setting. What is the difference between the binomial setting and the geometric setting?

Section 10.4 Analysis of Variance. Section 10.4 Objectives Use one-way analysis of variance to test claims involving three or more means Introduce (mention.

Random Probability Distributions BinomialMultinomial Hyper- geometric

Chapter 9: Joint distributions and independence CIS 3033.

The Poisson Distribution. The Poisson Distribution may be used as an approximation for a binomial distribution when n is large and p is small enough that.

In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n.

Practice Problems Actex 10. Section #1 An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for.

Combinatorial Principles, Permutations, and Combinations

Review of Risk Management Concepts

6-4 Large-Sample Confidence Intervals for the Population Proportion, p

Continuous Probability Distribution

The Poisson Probability Distribution

Functions and Transformations of Random Variables

Random Variables and Probability Distribution (2)

CONTINUOUS PROBABILITY DISTRIBUTIONS CHAPTER 15

LESSON 11: THE POISSON DISTRIBUTION

Additional notes on random variables

Additional notes on random variables

Statistical analysis and its application

Chapter 2. Random Variables

The Geometric Distributions

Uniform Probability Distribution

Distribution Function of Random Variables

Presentation transcript:

Practice Problems Actex 3, 4, 5

Section 3 -- #3 A box contains 4 red balls and 6 white balls. A sample of size 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls, given that at least 2 of the balls in the sample are white? Answer: 0.75

Section 3 -- #6 An insurance company determines that N, the number of claims received in a week, is a random variable with P(N=n) = 1/2 n+1, where n => 0. The company also determines that the number of claims received in a given week is independent of the number of claims received in any other week. Determine the probability that exactly seven claims will be received during a given two-week period. Answer: 1/64

Section 4 -- #5 In a small metropolitan area, annual losses due to storm, fire, and theft are independently distributed random variables. The pdf’s are: Storm: f(x) = e -x Fire: f(x) = (2/3)e -2x/3 Theft: f(x) = (5/12)e -5x/12 Determine the probability that the maximum of these losses exceeds 3. Answer: 0.414

Section 4 -- #10 An insurance company insures a large number of homes. The insured value, X, of a randomly selected home is assumed to follow a distribution with density function, f(x)=3x -4 for x>1 and equal to zero otherwise. Given that a randomly selected home is insured for at least 1.5, what is the probability that it is insured for less than 2? Answer: 0.578

Section 4 -- #16 The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function f, where f(x) is proportional to (10+x) -2. Calculate the probability that the lifetime of the machine part is less than 6. Answer:

Section 5 -- #7 A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. If a tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e. everything is made 20% more expensive), what will be the variance of the annual cost of maintaining and repairing a car? Answer: 374.4

Section 5 -- #23 A random variable has the cumulative distribution function: F(x)= 0 for x < 1 (x 2 -2x+2)/2 for 1 <= x < 2 1 for x => 2 Calculate the variance of X. Answer: 5/36