Questions and Answers
What does a probability model describe?
What is a random variable?
A variable that takes numerical values to describe the outcomes of a chance process.
The _____ of a random variable gives its possible values and their probabilities.
probability distribution
What are the two types of random variables?
Signup and view all the answers
What is a discrete random variable?
Signup and view all the answers
Legitimate probability distribution requirements are that probabilities are between _____ and _____ and that they sum to _____
Signup and view all the answers
What does the symbol ∑xipi represent?
Signup and view all the answers
What is the standard deviation of a discrete random variable represented by?
Signup and view all the answers
Situations that involve measuring something often result in a __________ random variable.
Signup and view all the answers
The __________ X takes on all values in an interval of numbers.
Signup and view all the answers
A continuous random variable Y has ___________ possible values.
Signup and view all the answers
What calculation should be used when evaluating normal probability distributions?
Signup and view all the answers
If knowing whether any event involving X alone has occurred tells us nothing about the occurrence of any event involving Y alone, then X and Y are ___________.
Signup and view all the answers
Two types of random variables are _____ and _____
Signup and view all the answers
When the same chance process is repeated several times, we consider the random variables called __________ random variables.
Signup and view all the answers
What arises when we perform several independent trials of the same chance process?
Signup and view all the answers
Which of the following are conditions for a binomial setting?
Signup and view all the answers
The count X of successes in a binomial setting is a _______. The probability distribution of X is called _________.
Signup and view all the answers
Study Notes
Probability Model
- Defines possible outcomes of a chance process and their associated likelihoods.
Random Variable
- A numerical value representing the outcome of a chance process.
Probability Distribution
- Provides a list of possible values for a random variable along with their associated probabilities.
Types of Random Variables
- Two main types are discrete and continuous random variables.
Discrete Random Variable
- Can list all possible outcomes and assign probabilities to each.
- Represents countable outcomes.
Probability Distribution Requirements
- Legitimate probability distributions have probabilities ranging from 0 to 1 and must sum to 1.
Mean/Expected Value
- Calculated using the formula ∑xipi for a discrete random variable.
Important Contextual Terms
- Include phrases like "in the long run," "about," and "on average" to provide context in problem interpretation.
Standard Deviation
- For a discrete random variable, calculated using √∑(xi - µx)²pi.
Continuous Random Variable
- Arises from measurements; can take on all values within an interval.
Probability Distribution of Continuous Variables
- Described by a density curve where the probability of an event is the area under the curve for corresponding values.
Infinite Values
- A continuous random variable has infinitely many possible outcomes.
Normal Probability Distributions
- Evaluated using the normalcdf function.
Independent Random Variables
- Two random variables are independent if the occurrence of events involving one does not affect the other.
Types of Random Variables (Binomial and Geometric)
- Binomial random variables count specific outcomes over a fixed number of trials, while geometric variables count the number of trials until the first success.
Binomial Setting
- Occurs during independent trials of the same chance process where the number of successes for a specific outcome is recorded.
Conditions for Binomial Setting
- Must meet four criteria: Binary outcomes, Independent trials, Fixed Number of trials, and Success definition.
Binomial Distribution
- The count of successes in a binomial setting is a binomial random variable; its probability distribution is termed binomial distribution.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers key concepts in probability models and random variables, including their definitions and types. You will explore probability distributions, expected values, and the characteristics of legitimate distributions. Test your understanding of these foundational principles in probability theory.
