Expected Value Practice

Front

What is the expected value in probability?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by its probability of occurrence.

Front

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

Back

To calculate the expected value (E) of a discrete random variable, use the formula: E(X) = Σ [x * P(x)], where x is a value and P(x) is the probability of that value.

Front

What is a discrete random variable?

Back

A discrete random variable is one that can take on a countable number of distinct values, often representing counts or whole numbers.

Front

What is a continuous random variable?

Back

A continuous random variable can take on an infinite number of values within a given range, often representing measurements.

Front

If a household has a 30% chance of having 1 child, a 43% chance of having 2 children, and a 27% chance of having 3 children, what is the expected number of children?

Back

The expected number of children is calculated as: E(X) = (1 * 0.30) + (2 * 0.43) + (3 * 0.27) = 1.97.

Front

What is the expected number of cars in an American household if the average is 1.75?

Back

The expected number of cars is simply the average, which is 1.75.

Front

Define probability distribution.

Back

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

Front

What is the difference between expected value and median?

Back

The expected value is the average of all possible outcomes weighted by their probabilities, while the median is the middle value when outcomes are arranged in order.

Front

How does the law of large numbers relate to expected value?

Back

The law of large numbers states that as the number of trials increases, the sample mean will converge to the expected value.

Front

What is the formula for expected value in a probability table?

Back

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