Expected Value Practice

Front

What is the expected value in probability and statistics?

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 of a discrete random variable, multiply each possible value by its probability and sum all these products.

Front

What is a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

Front

What does it mean if the expected value is negative?

Back

If the expected value is negative, it indicates that, on average, you are expected to lose money in that scenario.

Front

What is a fair game in terms of expected value?

Back

A fair game is one where the expected value is zero, meaning that neither the player nor the house has an advantage.

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on any value within a given range or interval.

Front

What is the expected value of a fair die roll?

Back

The expected value of a fair die roll is 3.5, calculated as (1+2+3+4+5+6)/6.

Front

How do you interpret the expected value in a gambling scenario?

Back

In a gambling scenario, the expected value helps determine whether a bet is favorable or unfavorable based on the potential outcomes and their probabilities.

Front

What is the formula for expected value in a lottery scenario?

Back

The expected value in a lottery scenario is calculated by summing the products of each prize's value and its probability, then subtracting the cost of the ticket.

Front

What is the significance of the law of large numbers in relation 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.