Expected Value Practice

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.

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

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

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

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

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

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

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

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.

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