Prob & Stat Ch 4 Review - Discrete, Continuous, Binomial

Front

What is a discrete random variable?

Back

A discrete random variable is a type of variable that can take on a countable number of distinct values. Examples include the number of students in a class or the number of phone calls received.

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on an infinite number of values within a given range. Examples include height, weight, and temperature.

Front

What is the probability of getting exactly 3 correct answers when guessing on a 6-question multiple choice test with 4 options each?

Back

0.132

Front

What is a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take. The sum of all probabilities must equal 1.

Front

What are the conditions for a binomial experiment?

Back

1. There are a fixed number of trials. 2. Each trial has two possible outcomes (success or failure). 3. The trials are independent. 4. The probability of success is the same for each trial.

Front

Is the experiment of shuffling a deck of cards and drawing 5 cards without replacement a binomial experiment?

Back

No, because there are more than 2 outcomes for each trial.

Front

How do you calculate the standard deviation of a probability distribution?

Back

Standard deviation is calculated using the formula: σ = √(Σ [p(x) * (x - μ)²]), where μ is the mean of the distribution.

Front

What does it mean if the sum of p(x) does not equal 1 in a probability distribution?

Back

It means that the distribution is not valid, as all probabilities must sum to 1.

Front

What is the formula for the binomial probability?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

Front

What is the difference between independent and dependent events in probability?

Back

Independent events are those whose outcomes do not affect each other, while dependent events are those where the outcome of one event affects the outcome of another.