What is the expected value of a function of a random variable?

The expected value of a random variable is denoted by E[X]. The expected value can be thought of as the “average” value attained by the random variable; in fact, the expected value of a random variable is also called its mean, in which case we use the notation µX. (µ is the Greek letter mu.)

How do you find the expected value of a product of a random variable?

The expected value of the sum of several random variables is equal to the sum of their expectations, e.g., E[X+Y] = E[X]+ E[Y] . On the other hand, the expected value of the product of two random variables is not necessarily the product of the expected values.

What is the expected value of a discrete random variable it is the?

For a discrete random variable the expected value is calculated by summing the product of the value of the random variable and its associated probability, taken over all of the values of the random variable.

How do you find the expected value of a variable?

Formula for the Expected Value of a Binomial Random Variable The formula for the Expected Value for a binomial random variable is: P(x) * X.

What is the expectation function?

Using expectation, we can define the moments and other special functions of a random variable. Definition 2 Let X and Y be random variables with their expectations µX = E(X) and µY = E(Y ), and k be a positive integer. 1. The kth moment of X is defined as E(Xk). If k = 1, it equals the expectation.

What is the meaning of the expected value of a variable?

The expected value of a random variable is the weighted average of all possible values of the variable. The weight here means the probability of the random variable taking a specific value.

What is the expected value and what does it measure how is it computed for a discrete probability distribution?

The expected value (EV) is an anticipated value for an investment at some point in the future. In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

What is the expected value of the probability distribution of a random variable?

What is meant by a random variable?

Key Takeaways. A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment’s outcomes. A random variable can be either discrete (having specific values) or continuous (any value in a continuous range).