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Conditional Probability Distribution

     A conditional probability distribution occurs when you have two random variables that are jointly distributed. This means that if we have two variables A and B, knowledge of one of the two variables will give some knowledge of the other variable. Then, the conditional probability distribution is the probability distribution function of one of the two variables given the other variable. For example, the probability of A equal to any 'a' given B = b would be described by the following:

This is the case for discretely distributed values of A and B. If instead, the distribution was continuous, then we would have to use the conditional density function. In which case you would get:

Where the numerator gives the joint density between A = a and B = b, and the denominator is the marginal density.


Standard normal distribution and empirical rule

Probability, Sampling Distributions, and Inference 1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours? 2) The lifetimes of light bulbs of a particular type are normally distributed with

How Many People to Survey?

How Many People to Survey? Poll results are prevalent in the media, especially leading up to elections, as are reports on surveys done by universities and research groups. The survey results of small groups of people are used to portray a general consensus about a population. Do you ever wonder how many people should be in

Exercises for improving flexibility in each joint in the body

I need assistance solving these problem exercises in excel format. CHAPTER 8 EXERCISE 2 The following is a list of 29 hospitals in the Cincinnati (Ohio) and Northern Kentucky region. The hospitals are identified by numbering them 00 through 28. Also included is whether the hospital is a general medical/surgical hospital (M/S

Normal distribution and normal approximation

[1] A particular airline has 10:00 a.m. flights from San Francisco to New York, Atlanta, and Miami. The probabilities that each flight is full are 0.60, 0.40, and 0.50 respectively, and each flight is independent one another. a) What is the probability that all flights are full? b) What is the probability that only the New Yo

Merit for a Lawsuit: Sexually Discriminatory Hiring Practices

The (entirely fictitious) University of South Central Maryland (USCM) is being sued for sexually discriminatory hiring practices. Last year, they hired two classes of employees: administrative staff and academic staff. They received 750 applications from women for administrative staff positions, of which they hired 250, and 2

Interval Construct/Estimate a Population Mean/Estimate the Value of a Parameter

22. You Explain It! Superstition A USA Today/ Gallup poll asked l006 adult Americans how much it would bother them to stay in a room on the 13th floor of a hotel. Interestingly, 13% said it would bother them. The margin of error was 3 percentage points with 95% confidence. Which of the following represents a reasonable interpret

Calculating probability under a standard normal curve

We are estimating the spares requirement for a radar power supply. The power supply was designed with a mean (μ) life of 6500 hours. The standard deviation (σ) determined from testing is 750 hours. What is the likelihood that a power supply would fail in less than 4880 hours?

Calculating probability that a stock gained value and lost value

The major stock market indexes had mixed results in 2011. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 0.00%. The mean one-year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was -1.8% Historically, the one-year returns are approximately normally distribu

Using the Normal Approximation to the Binomial

According to study done by Nick Wilson of Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing was 0.267. Suppose you sit on a mall bench and observe 200 people pass by as they sneeze. 1) Use the normal approximation to the binomial to find the probability of observing

Poisson distribution and other probability tests

PROBABILITY Question 1 A company employs 400 salespeople. Of these, 83 received a bonus last year, 100 attended special training program at the beginning of last year, and 42 both attended the special sales training and received a bonus. (Note: Bonus was based totally on sales performance.) a) What proportion o

Conditional probability relationships

As a part of your proposals. you need to submit demographic information to help demonstrate that the location chosen by the management teams will be a good investment. You have collected the following data sample of 2000 customers (specifically. the person paying the bill) on age and gender. (Please note: The bins used were dict

Conditional Probability: Population Obesity and Teenage Pregnancies

1.a) Overweight? Choose an American adult at random. Define two events: A= the person chosen is obese B= the person chosen is overweight but not obese According to the 2007 National Health Interview Survey, P(A)=0.26 and P(B)=0.35. Explain why events A and B are disjoint. 1. b) Say in plain language what th


A box contains six parts. Two of the parts are defective and four are ok. If three of the six parts are selected from the bin, how large is the sample space? Which counting rule did you use, and why? For this sample space, what is the probability that exactly one of the three sampled parts is defective? A business has 20 emp

Caterpillar Corporation

The Caterpillar Corporation depicts the current status for various classifications of equipment used in a Caterpillar manufacturing plant. The company categorizes equipment usage as Low, Medium, or High, depending upon the number of expected manufacturing applications applicable to its use. Equipment is also subject to availabil

Conditional Probability for efficacy of three drugs to treat headaches

See attached file for table. Which Probability formula should be used? Please explain. A researcher wants to prove the efficacy of three drugs to treat headaches. Results are given in the following table. If one of these subjects is randomly selected: 12- Find the probability that the subject had a headache given that

Calculating Conditional and Unconditional Probabilities

The probability of having disease X in the general population is only .05. The Sagman Test is a newly discovered method for early detection. Of those who have disease X, the test indicates the disease for 90% of them. Of those who do not have the disease, the test indicates no disease for 90% of them. Is the test a good predicto

Conditional probability

A local beer producer sells two types of beer, a regular brand and a light brand with 30% calories. The company's marketing department wants ti verify that its traditional approach of appealing to local white collar workers with light beer commercials and applealing to local blue-collar workers with regular beer commercials is i

Conditional Probability and Couples Watching TV

Please help with the following problems. Given that men and women who are married to each other watch a TV in the following proportions: Watch show: Male = 0.600 Female = 0.550 And that the probability a man watches the show if the woman is watching it is: 65% a) Find the probability that a man

Stocks: Expected Return and Standard Deviation

You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for $1000 investment in each stock under four different economic conditions has the following probability distribution: Returns Probability Economic Condition Stock X (in $'s) Stock Y (in $'s) 0.1 Recession - 50 - 100

Statistics: Probability, Counting, Multiplication Rule, Addition Rule

Section 3.1: Basic Concepts of Probability and Counting 1. License plates are made using 2 letters followed by 3 digits. How many different plates can be made if repetition of letters and digits is allowed? (References: example 4 page 135, end of section exercises 13 - 16 page 142 and 35 - 36 page 144) 2. In 2005 the


Bachelors Masters Professional Doctorate Total Female 986 411 52 32 1481 Male 693 260 45 27 1025 Total 1679 671 97 59 2506 Use this data: counts of degrees earned in the U.S. 2010-2011 (in thousands) to answer the following questions a) What is the probability that a randomly chosen degree recipient is a

Probability: Executive reads Time or US News; checking & savings, colored marbles

A Survey of top executives revealed that 35 percent of them regularly read Time magazine, 20 percent read Newsweek, and 40 percent read U.S. News and World Report. Ten percent read both Time and U.S. News and World Report. What is the probability that a particular top executive reads either Time or U.S. News and World Report

Probabilities: stock; WSJ advertisement; defective microprocessor; product success

2-77 Two stocks A and B are known to be related in that both are in the same industry. The probability that the stock A will go up in price tomorrow is 0.20, and the probability that both stocks A and B will go up tomorrow is 0.12. Suppose that tomorrow you find that stock A did go up in price. What is the probability that sto

Decision Tree

Liz has a small shop where she sells shirts and other tops. Unexpectedly the local high school basketball team has reached the state semi-finals. A few days before the game a supplier offers her a consignment of either 500 or 1000 of the team's shirts at a good price. She must make a decision right away. If the team reaches the

If a traveler is selected at random (from this group of 150 travelers), find the probability that P (The traveler is not Canadian and speaks French as the first language.) If a traveler is selected at random (from this group of 150 travelers), find the probability that P(The traveler is not Canadian, given that the first language is French.)

3. (TCO 5) The Canadian Services office did a survey of 150 travelers in which they asked if the traveler's first language was French or English. Another question asked was whether the traveler was Canadian born. The results follow. Canadian Not-Canadian Raw Totals English 15 50 65 French 65 20 85 Totals 80 70 150

Probabilities & Conditional Probabilities

Please show calculation as to how answer was gotten. Thank you. The availability of venture capital provided by big boost in funds available to companies recent years. According to Venture Economics, 2,000 venture capital disbursements were made in 1999. Of these, 334 were to companies in California, 490 were to companies

Conditional probability and variable type

Using the table Blood Alcohol Level of Victim Age A0.00% B0.01-09% C¡Ý0.10% D 0-19 142 7 6 155 E 20-39 47 8 41 96 F 40-59 29 8 77 114 G 60 or over 47 7 35 89 265 30 159 454 Calculate the conditional probability of C given each of the age groups, or P(C|D), P(

Respecity jar contents to make the jars statistically independent.

You have 4 jars. In the largest jar you have three balls numbered 1 to 3. Then you have 3 colored jars. Jar 1 has a red ball and two orange balls. Jar 2 has one orange ball and 2 red balls. Jar 3 has a red ball, an orange ball and a yellow ball. There are two random variables X and Y w/ X being the draw of a single numbered ba