A random variable in probability theory is a variable that takes on some value subject to chance. Random variables are also known as stochastic variables. So, a random variable does not have a set value. Instead it can take on a set of values. Each value in the set is associated with a certain probability that the random variable will take on that value. For example, the result of a dice throw can be thought of as a random variable. It has no fixed value, but it can take on any of the values 1, 2, 3, 4, 5, or 6. Each of these values has an associated probability of one sixth. This combination of probability and values makes up a probability distribution of the random variable. The above dice example is an example of a discrete random variable whereby each value is discretely separated from the next. Conversely, we can also have continuous random variables such as time. The probability distribution for a discrete random variable is called a probability density function.

# Random Variables

### Probability Axioms and Counting

Question1: Probability Axioms Assume that P(A) = 0.5, P (A ∩ C) = 0.18, P(C) = 0.4, P(B) = 0.4, P (A ∩ B ∩ C) = 0.06, P (B ∩ C) = 0.18, and P (A ∩ B) = 0.15. Calculate the following probabilities: a. P (A ∪ B ∪ C) b. P (A' ∩ (B ∪ C)) c. P ((B ∩ C)' ∪ (A ∩ B)') d. P (A/ (A ∩ C)) Question 2: Cou

### Calculating confidence interval for proportions

An interactive poll found out that 330 adults of 2,396 adults over the age of 18 have at least 1 tattoo. A) Obtain a point estimate of the proportion of adults that have at least 1 tattoo. p̂=____? B) Construct a 90% confidence interval for the proportion of adults that have at least 1 tattoo. Select the correct choice be

### Interval for population proportion and interpretation

In a trial of 185 patients who were given 10-mg of a drug daily, 48 reported headaches as a side effect. A) Obtain a point estimate population proportion of patients who received 10-mg of a drug daily and reported headaches as a side effect. p̂= _____________? Round to two decimal places as needed B) Verify that the requi

### Sampling Methods

I am having problems with the problems below, Can you help with them. 1. Define the following terms in your own words. • Population • Sample • Bias • Design • Response bias 2. Define and provide an example for each design method. • Simple random sampling • Systematic sampling • Stratified sampl

### Descriptive Statistics Frequency..

Hello, I need help with the problems below. 1. The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean? 99 34 86 57 73 85 91 93 46 96 88 79 68 85 89 2. The scores for math test #3 we

### Descriptive Statistics

1. Describe the measures of central tendency. Under what condition(s) should each one be used? 2. Last year, 12 employees from a computer company retired. Their ages at retirement are listed below. First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year. 55 77 64 77 69 63 62 64 8

### Probability of Event Occurring

I need help with the problems below. 1. In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who

### Pen production problem using Linear Programming technique

OPRE 315: Homework 3 1. The Charm City Manufacturing makes four models of ball point pens. Requirements for each lot of pens for each model are given below. Economy Model Super Model Luxury Model Premium Model Available Plastic 3 4 4 4 100 units Ink Assembly 3 4 4 6 120 units Molding Time 4 3 5 8 140 hours

### Directed Acyclic Graphs, Hazard Ratios, Confounding

Directed Acyclic Graphs (DAGs) To complete this assignment, please review the article by Shrier and Platt (2008), located in the Learning Resources. You may use any drawing tools available to you to create the DAGs requested below, although it does not need to be sophisticated software; for example, Microsoft Word's Insert Shap

### Probability Concepts in Business Decisions

I need assistance responding to the discussion question below: Probability is a very interesting concept. It's one where you may never think about calculating or using it in real life. However, we tend to use it more frequently than we believe. I use probability every day, but I never calculate the probability using a formula

### Theoretical and Experimental Probability

1. Explain the difference between theoretical probability and experimental probability with examples. 2. In a Physics class, 25 students own their own computer and 5 do not. If one of the students is randomly chosen, find the probability of someone who own a computer. 3. Listed below are the selling prices (in thousands of

### Nature and Assumption of the Normal Distribution

What is a real example of Normal Distribution (other than height) and what makes it really normal? 1) Can everything be normally distributed, that is, fall along a 'bell curve'? 2) More Importantly, WHY do we make the 'assumption of normality' for inferential statistics?

### Analyzing a Probability Experiment

Please help show me how to do a tree diagram for this problem and proving step-by-step solution to make sure the rest of the problem is correct. 14. Suppose you perform a probability experiment in which you toss a fair coin and then roll a fair number cube with the faces labeled with numbers 1 through six. a. Draw a tree

### Testing the Significance Level and Interpreting the P-Value

The Butts Power Company forecasts that the mean residential electricity usage per household will be 700 kwh next January. In January, the company selects a simple random sample of 50 households and computes a mean and standard deviation of 715 and 50, respectively. Test at the .05 significance level to determine whether Butts

### Compute Probability and Conditonal Probability

Eye Colour Hair Colour Brown Blue Green Hazel Blond 30 18 7 2 57 Brown 74 28 10 7 119 Red/Auburn 17 15 5 3

### Steps on determining the equation for unit formulation

Given the following information, determine the equation for the unit formulation. (Round intermediate calculations to 4 decimal places) Unit Number (X) Unit Cost (Y) $ 1 1000.00 2 840.00 3 758.55 4 705.60 Y = (1000)(X)0.8700

### Steps on calculating the probability under the standard normal distribution

1. The average annual rainfall in a certain region is normally distributed with a mean of 31.3 inches and a standard deviation of 7.2 inches. A. In any given year, what is the probability that the amount of rain will exceed 24.82 inches? B In any given year, what is the probability that the amount of rain will be between 31.

### Inventory Management and Control for Apple Inc.

PROBABILITY AND RANDOMNESS Session Long Project For the session long project discuss how probabilty or randomness impacts your organization, such as scheduling, order shipments, inventory control, etc. You may choose one of your favorite organizations (APPLE INC). Collect your own data to support your argument and assess cult

### Step-by-Step Method for the Calculation of Probabilities

1. You pull out one randomly taken card from a standard deck of cards. Find the probability that the card is not a Queen. Use formula: P(not A) = 1 - P(A) Standard deck of cards has 4 Queens out of total 52 cards. Simplify fraction 2. Box has 10 M&M candies: 5 red and 5 blue. Two candies are taken from this box. Find the prob

### mean, median, and mode of newspapers sold

3. A retail store manager kept track of the number of car magazines sold each week over a 10-week period. The results are shown below. 27 30 21 62 28 18 23 22 26 28 a. Find the mean, median, and mode of newspapers sold over the 10-week period. b. Which measure(s) of central tendency best represent the data?

### creating a stem plot for the data and then finding the mean of data

2. Last year, 12 employees from a computer company retired. Their ages at retirement are listed below. First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year. 55 77 64 77 69 63 62 64 85 64 56 59

### Describing data as it keeps track of time

Describe the data you are going to collect and how you are going to keep track of the time. Within the paper, incorporate the concepts we are learning in the module including (but not limited to) probability theory, independent and dependent variables, and theoretical and experimental probability. Discuss your predictions of wha

### Computing the Probability of Choice

A color candy was chosen randomly out of a bag. Below are the results: Color Probability Blue 0.30 Red 0.10 Green 0.15 Yellow 0.20 Orange ??? a. What is the probability of choosing a yellow candy? b. What is the probability that the candy is blue, red, or green? c. What is the probabil

### Computing Probability and Theoretical Probability

Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails? Answer the following problem showing your work and explaining (or analyzing) your results.

### Finding the Probability of Occurrence

A poll was taken to determine the birthplace of a class of college students. Below is a chart of the results. a. What is the probability that a female student was born in Orlando? b. What is the probability that a male student was born in Miami? c. What is the probability that a student was born in Jacksonville? Gender

### Basic Statistics: Calculations for Hypothesis Testing & Probability

Hello, I'm having difficulties setting up the problems, I'm understanding the formulas and concepts, but I would really appreciate your help! For Questions 3 & 4, complete the following: a) State the null and alternate hypotheses. Will we use a left-tailed, right-tailed, or two-tailed test? What is the level of signific

### Sample of Checking Randomly

An analyst processes one item every 30 minutes, so 80 items are completed in her first day of work. Her manager checks her work by randomly selecting an hour of the day, then reviewing all the items she completed that hour. Does this sampling plan result in a random sample? Simple random sample? (A) No, because each item does

### Difference Between Mean and Median

In the business world, the mean salary is often used to describe the salaries of employees of a company. However, the median salary may be a better measure of the salaries than the mean. Which is the better measure of central tendency? Why?

### The "birthday problem" in probability theory

One of the most famous probability calculations is called the "birthday problem". In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. Ignoring leap year and assuming that there are only 365 days in a

### Random variables in public health industry

For the public health industry, describe some examples of a random variable