5. Binomial Distribution & Discrete Random Variables

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

Given the following probability distribution for the discrete random variable $y$: $\begin{array}{cccc}y& 1& 2& 3\\ P\left(y\right)& 0.2& 0.5& 0.3\end{array}$ What is the expected value of $y$?

Which of the following is an example of a binomial random variable?

Given the following table showing the possible values of a random variable $X$ and their probabilities: Value of $X$: $0$, $1$, $2$, $3$; Probability: $0.1$, $0.3$, $0.4$, $0.2$. Is the random variable $X$ discrete or continuous? Explain your answer.

Given that $x$ has a Poisson distribution with parameter $\lambda$, which of the following is the correct expression for the probability that $x$ equals $k$?

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.

c. What is the probability that a randomly selected mother aged 50 to 54 who had a live birth in 2017 was having her sixth child or more?

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

If the discrete random variable $x$ is uniformly distributed over the integers from $10$ to $20$ inclusive, what is the probability that $x$ equals $15$?

A student is analyzing different types of variables in a statistics class. Which of the following below is a discrete random variable?

A factory produces lightbulbs in batches of 50. The probability distribution for the number of defective lightbulbs in a randomly selected batch is shown below. Find the expected value.

A company tracks the number of complaints they receive, where the random variable X is the number of complaints received daily. Find the variance & standard deviation of this distribution.

Identifying Discrete and Continuous Random Variables. In Exercises 5 and 6, refer to the given values, then identify which of the following is most appropriate: discrete random variable, continuous random variable, or not a random variable.

a. IQ scores of statistics students

b. Exact heights of statistics students

c. Shoe sizes (such as 8 or 8½) of statistics students

d. Majors (such as history) of statistics students

e. The number of rolls of a die required for a statistics student to get the number 4

Discrete or Continuous? Is the random variable given in the table from Exercise 1 discrete or continuous? Explain.