12/5 Probability Distributions Review (M4)

Front

What is a probability distribution?

Back

A probability distribution is a mathematical function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

Define discrete random variable.

Back

A discrete random variable is a type of variable that can take on a countable number of distinct values.

Front

Define continuous random variable.

Back

A continuous random variable is a type of variable that can take on an infinite number of values within a given range.

Front

What is the expected value in probability?

Back

The expected value is the average of all possible outcomes of a random variable, weighted by their probabilities.

Front

What is the formula for calculating the expected value?

Back

E(X) = Σ [x * P(x)], where x is a possible outcome and P(x) is the probability of that outcome.

Front

What does it mean to have a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Front

How do you calculate the probability of getting exactly k successes in n trials?

Back

Use the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

What is the binomial coefficient?

Back

The binomial coefficient, denoted as (n choose k), is the number of ways to choose k successes in n trials and is calculated as n! / (k!(n-k)!).

Front

What is the significance of standard deviation in a data set?

Back

Standard deviation measures the amount of variation or dispersion in a set of values.