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Questions and Answers
What is a random variable?
What is a random variable?
- A variable that is always constant
- A known value that does not change
- An unknown quantity whose value depends on chance (correct)
- A variable with a fixed probability
What is a probability distribution table?
What is a probability distribution table?
The table that summarizes the possible values of a discrete random variable and their corresponding probabilities.
What is a probability histogram?
What is a probability histogram?
A graph that displays the possible values of a discrete random variable on the horizontal axis and their corresponding probabilities on the vertical axis.
A discrete random variable can list all its possible values.
A discrete random variable can list all its possible values.
A continuous random variable can have non-countable values.
A continuous random variable can have non-countable values.
What is the expected value of a random variable?
What is the expected value of a random variable?
What is the standard deviation of a random variable?
What is the standard deviation of a random variable?
What are Bernoulli trials?
What are Bernoulli trials?
What is a binomial random variable?
What is a binomial random variable?
In a binomial experiment, there are more than two possible outcomes.
In a binomial experiment, there are more than two possible outcomes.
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Study Notes
Random Variables
- A random variable is an unknown quantity influenced by chance.
- Two main types of random variables exist: discrete and continuous.
Discrete Random Variables
- A discrete random variable has a finite or countable set of possible values.
- For discrete random variables, a probability distribution table summarizes possible values and their associated probabilities.
Probability Representations
- A probability histogram visually represents possible values of a discrete random variable, plotting values on the horizontal axis and probabilities on the vertical axis.
Continuous Random Variables
- A continuous random variable can take any value within a continuous interval, making it distinct from discrete variables.
Expected Value
- The expected value of a random variable reflects the average outcome over numerous experiments, providing a measure of central tendency.
Standard Deviation
- The standard deviation of a random variable quantifies the amount of variation or dispersion from the expected value. It is derived from the square root of the average of squared deviations from the mean.
Bernoulli Trials
- Bernoulli trials are sequences of identical independent experiments, with a binary outcome (success or failure) across n trials.
Binomial Random Variables and Experiments
- A binomial random variable counts the number of successes in n Bernoulli trials, adhering to a fixed number of trials and consistent success probability.
- A binomial experiment has two outcomes: success (with probability P(S) = p) and failure (with probability P(F) = 1 - p).
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