Flashcard 8.1 2024

Front

What is the expected value in probability?

Back

The expected value is the average of all possible outcomes of a random variable, weighted by their probabilities.

Front

How do you calculate the expected value of a discrete random variable?

Back

Multiply each possible outcome by its probability and sum all these products.

Front

What is a discrete random variable?

Back

A discrete random variable is one that can take on a countable number of distinct values.

Front

What is a continuous random variable?

Back

A continuous random variable can take on an infinite number of possible values within a given range.

Front

What is a probability distribution?

Back

A probability distribution describes how probabilities are distributed over the values of a random variable.

Front

What are the properties of a valid probability distribution?

Back

1. All probabilities must be between 0 and 1. 2. The sum of all probabilities must equal 1.

Front

What is the formula for calculating expected value?

Back

E(X) = Σ [x * P(x)], where x is a possible outcome and P(x) is the probability of that outcome.

Front

What does it mean if the sum of p(x) does not equal 1?

Back

It means that the set of probabilities does not form a valid probability distribution.

Front

Give an example of a discrete random variable.

Back

The number of students in a classroom.

Front

Give an example of a continuous random variable.

Back

The time it takes to complete a test.