Can expectation be a random variable?

Conditional expectation, E(X |Y ), is a random variable with randomness inherited from Y , not X.

Is the expectation of a random variable a constant?

The expected value of a constant is just the constant, so for example E(1) = 1. Multiplying a random variable by a constant multiplies the expected value by that constant, so E[2X] = 2E[X].

What is not a random variable example?

The identity function X on R (i.e. X(r)=r for all r∈R) is not a random variable for the set of outcomes (sample space) Ω=R and the set of events F= {all (at most) countable subsets of R and their complements}. The peculiarity of this example is that, for all r∈R, (X=r) is an event, yet (X

What is the expectation 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.

Is expectation same as mean?

While mean is the simple average of all the values, expected value of expectation is the average value of a random variable which is probability-weighted. While mean does not take into account probability, expectation considers probability and it is probability-weighted.

Can expectations be negative?

Expected value is the average value of a random variable over a large number of experiments . Since expected value spans the real numbers, it is typically segmented into negative, neutral, and positive valued numbers.

What are expectation of a function of random variable?

The expectation of Bernoulli random variable implies that since an indicator function of a random variable is a Bernoulli random variable, its expectation equals the probability. Formally, given a set A, an indicator function of a random variable X is defined as, 1A(X) = { 1 if X ∈ A 0 otherwise .

What is the expectation of random variable L?

The expected value of a random variable is the weighted average of all possible values of the variable.

Why is expected value of random variable equal to mean?

Answer: The expected value of a random variable is its mean . It is the value you expect to obtain if you conduct an experiment whose outcomes are represented by the random variable. It is the weighted average of all possible values where the probabilities of occurrence of the values are the weights.

What is the expected value of a discrete random variable?

More practically, the expected value of a discrete random variable is the probability-weighted average of all possible values. In other words, each possible value the random variable can assume is multiplied by its probability of occurring, and the resulting products are summed to produce the expected value.

What is the formula for a random variable?

For a discrete random variable, the expected value, usually denoted as μ or E (X), is calculated using: μ = E (X) = ∑ x i f (x i) The formula means that we multiply each value, x, in the support by its respective probability, f (x), and then add them all together.

What is the formula for expectation?

The expectation is the expected value of X, written as E(X) or sometimes as μ. The expectation is what you would expect to get if you were to carry out the experiment a large number of times and calculate the ‘mean’. To calculate the expectation we can use the following formula: E(X) = ∑ xP(X = x)