What is a random variable?
A variable whose values are determined by the outcomes of a random phenomenon.
Random variables can be classified as discrete or continuous.
Define discrete random variable.
A random variable that can take on a countable number of distinct values.
Examples include the number of heads in coin flips.
Define continuous random variable.
A random variable that can take on any value within a given range.
Examples include measurements like height or weight.
What is a probability distribution?
A function that describes the likelihood of obtaining the possible values of a random variable.
It can be represented in a table, graph, or mathematical formula.
What does the mean of a probability distribution represent?
The average or expected value of the random variable.
It indicates the central tendency of the distribution.
What is the standard deviation of a probability distribution?
A measure of the dispersion or spread of the values of a random variable.
It quantifies how much the values typically deviate from the mean.
Define expected value.
The long-term average value of a random variable over many trials.
It is calculated as the sum of all possible values, each multiplied by its probability.
What is a binomial experiment?
A statistical experiment that has
* a fixed number of independent trials,
* each trial has two possible outcomes, success and failure
* there is a fixed probability p if sucess
* It asks how many sucesses there are
These outcomes are typically termed ‘success’ and ‘failure’.
What does the number of trials, n, refer to in a binomial experiment?
The total number of independent trials conducted in the experiment.
Each trial is assumed to be identical and independent.
What are independent trials?
Trials in which the outcome of one trial does not affect the outcome of another trial.
This is a key assumption in binomial experiments.
Define successes and failures in a binomial experiment.
The two outcomes of each trial, where ‘success’ is the desired outcome and ‘failure’ is the non-desired outcome.
The terms are context-dependent and can vary by experiment.
What is the probability of success in a binomial experiment?
The likelihood of obtaining a success on a single trial.
This value is denoted by p.
What is the probability of failure in a binomial experiment?
The likelihood of obtaining a failure on a single trial.
This value is denoted by q, where q = 1 - p.
What does the number of successes, r, represent in a binomial experiment?
The count of successful outcomes observed in n trials.
r can range from 0 to n.
What is the binomial coefficient?
A mathematical expression that determines the number of ways to choose r successes from n trials.
It is denoted as nCr and can be found in the PRB menu under math
What is the binomial probability distribution?
The probability distribution that gives the probabilities of obtaining r successes in n trials of a binomial experiment.
It is calculated using the binomial formula.
What is the mean for the binomial distribution?
The expected number of successes in a binomial experiment, calculated as n * p.
This describes the average outcome of successes across many trials.
What is the standard deviation for the binomial distribution?
A measure of variability in the number of successes, calculated as √(n * p * q).
It indicates how much the number of successes is expected to vary from the mean.
