Expected Value Calculator: Compute Mean of Random Variables
Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson. Most elementary courses do not cover the geometric, hypergeometric, and Poisson. Your instructor will let you know if he or she wishes to cover these distributions. Therefore, we expect a newborn to wake its mother after midnight 2.1 times per week, on the average. A men’s soccer team plays soccer zero, online casino curacao one, or two days a week. The probability that they play zero days is .2, the probability that they play one day is .5, and the probability that they play two days is .3.
For example, we might bet on red in roulette, and think about what our average gain would be if we play hundreds of games. The proportion is just a special case of an average, when the random variable takes only the values \(0\) or \(1\). So you can see that we can think of the average as the value we would predict for the random variable – some sort of typical or expected value. At its core, the expected value is a weighted average of all possible values that a random variable can take on, with each value being weighted according to its probability of occurrence. It forms the backbone of numerous disciplines, including but not limited to finance, economics, game theory, and insurance, among others.
Less work, more wins
Generally for probability distributions, we use a calculator or a computer to calculate μ and σ to reduce rounding errors. For some probability distributions, there are shortcut formulas for calculating μ and σ. In the next example, we will demonstrate how to find the expected value and standard deviation of a discrete probability distribution by using relative frequency. The Las Vegas casino Magnicifecto was having difficulties attracting its hotel guests down to the casino floor. The empty casino prompted management to take drastic measures, and they decided to forgo the house cut.
The expected value of $300 represents the average return you would expect from this investment in the long run. This means that if you were to make this investment many times under the same conditions, the average return would be $300. The Expected Value Calculator is designed to make complex probability calculations simple and accessible. Whether you need to find expected value for statistics homework, research analysis, or business decisions, our calculator provides instant, accurate results with detailed explanations. This means that, on average, you can expect to gain $2.50 per roll if you play this game many times. You are about to play a game in which you draw 3 ping-pong balls without replacement from a barrel.
This makes intuitive sense since if all variables are translated by a constant, the central or mean value should also be translated by the constant. The second theorem shows that scaling the values of a random variable by a constant \(c\) also scales the expected value by \(c\). We create another random variable, Z, by adding every element of X to its respective element from Y.
For a valid probability distribution, all probabilities must sum to exactly 1. If they don’t, you either have missing outcomes or incorrect probability assignments. Our calculator will alert you if probabilities don’t sum to 1 and help you identify the issue. An expected value of $108.50 doesn’t guarantee you’ll make exactly $8.50 profit. Instead, it tells you that if you made this same investment decision many times under identical conditions, your average outcome would be a gain of $8.50 per investment. The expected value is a key concept in probability, statistics, and related fields.
These properties make expected value a powerful tool for analyzing combinations of random variables. This means that if the company used this particular advertisement an infinite number of times, it would expect to lose $3.70 each time, on average. This means that if we invested in this particular investment an infinite number of times, we would expected a long-term average annual return of 3.75%.
How is standard deviation related to variance?
- This often occurs in situations involving losses or negative outcomes, such as in gambling or investment scenarios where losses are possible.
- Expected value tells you the central tendency (average outcome), while variance and standard deviation measure the spread or risk around that average.
- Expected value (EV) is a concept employed in statistics to help decide how beneficial or harmful an action might be.
- They felt that since the expected value of every game is 0, they should not be making or losing money in the long run.
The interactive visualizations and step-by-step calculations help develop intuition about probability concepts while providing accurate results for your statistical needs. The variance measures the spread of values around the expected value, and the standard deviation is the square root of the variance. The expected value of discrete random variable is determined by the sum of the product of each value with their respective probabilities.
How to Calculate the Expected Value?
This often occurs in situations involving losses or negative outcomes, such as in gambling or investment scenarios where losses are possible. Expected value is often used by businesses to calculate the expected return on advertising spending. For example, suppose in a certain game there is a 5% chance of winning $100, a 50% chance of winning $0, and a 45% chance of losing $20. Models the number of successes in a fixed number of independent trials, each with the same probability of success. Used for scenarios like coin flips, yes/no surveys, or pass/fail tests.
Find the long-term average or expected value, μ, of the number of days per week the men’s soccer team plays soccer. A life insurance actuary estimates the probabilities of \(X\), a person’s life expectancy, with the probability density function as described above. The below two theorems show how translating or scaling the random variable by a constant changes the expected value.