A Bernoulli random variable (rv) is a random variable with possible values of only 0 or 1. Consider a variable $L$ the on position is assigned a value of 1. Because the only possible values of $L$ are 0 and $\boxed{\phantom{0}}$, $L$ Use this approach to determine which of the following variables are examples of Bernoulli variables. (Select all $\text{O } X = 1 \text{ if a randomly selected car needs an oil change and } X = 0 \text{ otherwise.}$ $\text{O } X = \text{ the number of cars that need an oil change in a randomly selected parking lot and } X = 0 \text{ if there are}$ $\text{O } X = \text{ the amount of rainfall in inches on a randomly selected day and } X = 0 \text{ if there is none.}$ $\text{O } X = \text{ the number of items purchased by a randomly selected customer at an online store and } X = 0 \text{ if ther}$ $\text{O } X = 1 \text{ if a randomly selected day has more than 2 inches of rain and } X = 0 \text{ otherwise.}$ $\text{O } X = 1 \text{ if a randomly selected customer purchases more than 10 items at an online store and } X = 0 \text{ otherw}$
Added by Jill H.
Close
Step 1
These values represent the outcomes of a single trial of a Bernoulli experiment, which has only two possible outcomes (success or failure). Step 2: Fill in the blank. The definition states that a Bernoulli random variable has possible values of only 0 or 1. Show more…
Show all steps
Your feedback will help us improve your experience
Narayan Hari and 93 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Narayan H.
The simplest random variable (RV) follows the Bernoulli distribution. This is a RV with two possible values: success (which we think of as 1), which appears with probability p, and failure (0), which appears with probability 1 - p. a. Explain why the pmf can be written in this surprising way: f(x;p) = p^x(1 - p)^{1-x}. b. For many students, the above pmf feels like pure magic. Explain how you can come up with this if you happen to know the pmf for the Binom(n,p) distribution. c. Explicitly calculate the mean and variance of the Bernoulli RV with parameter p using the definitions of mean and variance. d. If X1,...,Xn are iid (independent and identically distributed) Bernoulli(p) RVs, and Y ~ Binom(n,p) is Binomial, write a formula that relates Y and the Xi s. Then, explain how the formula can help you easily remember the mean and variance of a Binomial RV.
Jon S.
Select the instances in which the variable described is binomial. A quality check on a particular product must meet five guidelines. All products are made in the same factory under the same conditions. The random variable represents the total number of products out of 35 tested that pass inspection. The probability of drawing a king in a standard deck of cards is 0.08. Seven cards are drawn without replacement. The random variable represents the total number of king cards observed. A coin flip has two outcomes: heads or tails. The probability of each outcome is 0.50. The random variable represents the total number of flips required to get tails. There are two banking options for customers of ABC Bank, checking or savings. The random variable represents the total number out of 567 customers with a checking account. Based on the parents' genetics, each of 6 children from a particular pair of parents has a 0.25 probability of having the O blood type. The random variable represents the total number of children from this pair of parents with the O blood type.
Adi S.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD