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?

In Exercises 1–4, find the indicated probability using the geometric distribution.

Find P(3) when p = 0.65

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.

Find the mean of the random variable x described in the preceding exercise.

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?

In your own words, describe the difference between the value of x in a binomial distribution and in the Poisson distribution.

Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.

Online Courses College students are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they take one or more online courses (based on data from Sallie Mae).

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.

What is the difference between a discrete random variable and a continuous random variable? Provide your own examples of each.

Identifying Probability Distributions In Exercises 27 and 28, determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why.