Statistics and Probability with Application

What is the difference between a discrete random variable and a continuous random variable?

• A discrete random variable takes all values in an interval of numbers while a continuous random variable has a fixed set of possible values with gaps between.
• A discrete random variable has a fixed set of possible values with gaps between while a continuous random variable takes all values in an interval of numbers.
• A discrete random variable takes only negative numbers while a continuous random variable takes both positive and negative numbers.
• A discrete random variable takes both positive and negative numbers while a continuous random takes only negative numbers.

What are the two types of random variables

• Discrete and Continuous
• Binary and Non-Binary
• Expected and Predicted
• Positive and Negative

A regular deck of cards has 4 aces. You are asked to pick one card from the deck. If the card you picked is an ace you win $5! However if you pick any other card, you lose $2. If you play this game many times, on average how much would you expect to win?

• About $1.46
• About $4.46
• About -$1.46
• About $3

Multiplying/Dividing each value of a random variable by a number x will...
I. Multiply/Divide the mean, median, quartiles, and percentiles by number x
II. Multiply/Divide the shape of the distribution by number x
III. Multiply/Divide the range, IQR, standard deviation by |x|

• I and II
• I and III
• II and III
• I, II, and III

The count of X successes in a binomial setting is a:

• Binary outcome
• Binomial probability
• Binomial distribution
• Binomial random variable

To find the mean of a binomial random variable

• Multiply the probability of success times the probability of failure.
• Multiply the number of trials times the probability of failure
• Multiply the number of trials times the probability of success.
• Multiply the number of trials times the probability of success times the probability of failure.

To find the mean/expected value for a geometric random variable

• Multiply the number of trials times the probability of success on each trial.
• Divide 1 by the probability of success on each trial.
• Multiply the number of trial times the probability of failure on each trial.
• Divide 1 by the probability of failure on each trial.

A  ____________ consists of repeated trials of the same chance process in which each trial results in a success or a failure, trials are independent, each trial has the same probability of success, and the goal is to count the number of trials until the first success occurs.

• Binomial setting
• Binomial distribution
• Geometric setting
• Geometric distribution

Suppose that a town is randomly selected from the state. Which of these pairs of random variables are most likely independent

• X= Average house size in acres and Y= Average weight of people living in that town
• X= Average house size in acres and Y= Average annual income
• X= Average height of people living in that town and Y= Average weight of people living in that town
• X= Average monthly mortgage payment and Y= Average annual income

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

• Binomial Random Variables
• Geometric Random Variables
• Independent Random Variables
• Linear Random Variable