5. Binomial Distribution & Discrete Random Variables

"Video Poker The following table shows the net winnings from a \$1 bet in a video poker game.

b. If a player expects to play 90 games in one hour, how much can the player expect to win or lose during that hour?"

$$Which of the following is an example of a discrete random variable?$$

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

For a random variable x, the word random indicates that the value of x is determined by chance.

A ______ random variable has either a finite or a countable number of values.

Given the following table showing the possible values of a random variable $X$ and their probabilities: Value of $X$: 0, 1, 2; Probability: 0.2, 0.5, 0.3. Is the random variable $X$ discrete or continuous? Explain your answer.

Which of the following is a criterion for a binomial probability experiment?

Which of the following variables is not continuous?

In Problems 9–14, determine whether the distribution is a discrete probability distribution. If not, state why.

Number of BirthsThe graph of the discrete probability distribution below represents the number of live births by a mother 50–54 years old who had a live birth in 2017.

b. What is the probability that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having either her fourth or fifth child?

In Exercises 9 and 10, find the expected net gain to the player for one play of the game.

It costs \$25 to bet on a horse race. The horse has a 1/8 chance of winning and a 1/4 chance of placing second or third. You win \$125 if the horse wins and receive your money back if the horse places second or third.

[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

a. Confirm that this represents a discrete probability distribution.

Which of the following can be represented by a $discreterandomvariable$?

Which of the following is a criterion for a binomial probability experiment?

Which of the following is not a discrete random variable?