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Discrete Random Variables: Section 5 Notes

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Discrete Random Variables: Section 5 Notes

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Questions and Answers

What is the main distinction between a variable and a random variable?

A variable depends on chance, while a random variable does not.

A random variable maps the sample space to real numbers, while a variable does not. (correct)

A random variable describes the likelihood of quantitative outcomes across an entire population, while a variable does not.

A variable is a statistical concept, while a random variable is not.

How are random variables typically denoted?

With symbols from the middle of the alphabet

With lowercase letters

With symbols from the beginning of the alphabet (correct)

With numbers

Why is it crucial to correctly identify a quantitative variable as either discrete or continuous?

To find probabilities in the same way for both types

To distinguish how probabilities are calculated for discrete and continuous random variables (correct)

To assign values to each possible outcome

To determine its sample space

Which of the following is NOT true regarding random variables?

Random variables are always denoted by lowercase letters. Signup and view all the answers

In what context are random variables and populations often used together?

In statistics Signup and view all the answers

What is a discrete random variable?

A variable with a finite number of outcomes in the sample space Signup and view all the answers

What is a common characteristic of a discrete random variable?

Outcomes can be represented in a list Signup and view all the answers

Which criteria must be met for a discrete random variable to exist?

Sum of all probabilities for individual outcomes must be equal to 1 Signup and view all the answers

What does the expected value of a random variable represent?

The mean of the variable weighted by probabilities Signup and view all the answers

How is the expected value of a general discrete random variable calculated?

$E(X) = \Sigma x_i \times P(X = x_i)$ Signup and view all the answers