# Are estimators random variables?

Last Update: April 20, 2022

This is a question our experts keep getting from time to time. Now, we have got the complete detailed explanation and answer for everyone, who is interested!

**Asked by: Gardner Runolfsdottir**

Score: 4.5/5 (18 votes)

An estimator is a special case of a statistic, a number computed from a sample. Because the value of the estimator depends on the sample, the estimator is **a random variable**, and the estimate typically will not equal the value of the

**any measured quantity of a statistical population that summarises or describes an aspect of the population**, such as a mean or a standard deviation. ... Thus a "statistical parameter" can be more specifically referred to as a population parameter.

## Are estimates random?

Being a function of the data, the **estimator is itself a random variable**; a particular realization of this random variable is called the "estimate". Sometimes the words "estimator" and "estimate" are used interchangeably.

## How do you estimate a random variable?

6 Linear MMSE Estimation of Random Variables. Suppose that we would like to estimate the value of an unobserved random variable X, given that we have observed Y=y. In general, our estimate ˆx is **a function of y ˆx=g(y)**. For example, the MMSE estimate of X given Y=y is g(y)=E[X|Y=y].

## Can a statistic be a random variable?

A statistic is a random variable (e.g. T): A statistic is any **function of the data** (unchanged from sample to sample). The data are described by random variables (of some suitable dimension). As any function of a random variable is itself a random variable, a statistic is a random variable.

## What are the two types of random variables?

There are two types of random variables, **discrete and continuous**.

## Random variables | Probability and Statistics | Khan Academy

**41 related questions found**

### Why do we use random variables?

In probability and statistics, random variables are **used to quantify outcomes of a random occurrence**, and therefore, can take on many values. Random variables are required to be measurable and are typically real numbers.

### What is the difference between variable and random variable?

A variable is a symbol that represents some quantity. A variable is useful in mathematics because you can prove something without assuming the value of a variable and hence make a general statement over a range of values for that variable. A random variable is a value that follows some **probability distribution**.

### What is the formula for finding the mean of a discrete random variable?

The mean μ of a discrete random variable X is a number that indicates the average value of X over numerous trials of the experiment. It is computed using the formula **μ=∑xP(x)**.

### How do you tell if a random variable is discrete or continuous?

A discrete variable is a variable whose value is obtained by counting. A **continuous variable** is a variable whose value is obtained by measuring. A random variable is a variable whose value is a numerical outcome of a random phenomenon. A discrete random variable X has a countable number of possible values.

### Why are estimators random?

An estimator is an assignment of a number (the estimate of the parameter) to each possible random sample of size n from the population. ... Because the value of the estimator **depends on the sample**, the estimator is a random variable, and the estimate typically will not equal the value of the population parameter.

### How much do estimators get paid?

Find out what the average Estimator salary is

Entry-level positions start **at $88,875 per year**, while most experienced workers make up to $175,000 per year.

### What are the two types of estimation?

There are two types of estimates: **point and interval**. A point estimate is a value of a sample statistic that is used as a single estimate of a population parameter.

### What is the similarities and differences between continuous and discrete variable?

Discrete variables are the variables, wherein the values can be obtained by counting. On the other hand, Continuous variables are the random variables that measure something. Discrete variable assumes independent values whereas continuous variable assumes any value in a **given range or continuum**.

### What are examples of discrete random variables?

**Examples of discrete random variables include:**

- The number of eggs that a hen lays in a given day (it can't be 2.3)
- The number of people going to a given soccer match.
- The number of students that come to class on a given day.
- The number of people in line at McDonald's on a given day and time.

### What is an example of a discrete variable?

Discrete random variables have numeric values that can be listed and often can be counted. For example, the **variable number of boreal owl eggs in a nest** is a discrete random variable. Shoe size is also a discrete random variable.

### Is random variable can be negative?

Yes, **they can be negative** Consider the following game. A fair 4-sided die, with the numbers 1; 2; 3; 4 is rolled twice. ... If we let X denote the (possibly negative) winnings of the player, what is the probability mass function of X? (X can take any of the values -3;-2;-1; 0; 1; 2; 3.)

### What are the 5 types of variables?

**Types of variables**

- Independent variables. An independent variable is a singular characteristic that the other variables in your experiment cannot change. ...
- Dependent variables. ...
- Intervening variables. ...
- Moderating variables. ...
- Control variables. ...
- Extraneous variables. ...
- Quantitative variables. ...
- Qualitative variables.

### What are the four types of variables?

Four Types of Variables

You can see there are four different types of measurement scales (**nominal, ordinal, interval and ratio**). Each of the four scales, respectively, typically provides more information about the variables being measured than those preceding it.

### What is variable example?

A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. **Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type** are examples of variables.

### Are features random variables?

The features are indeed **random variables** because we assume that their possible values are outcomes of a random phenomenon and they follow a specific distribution that we might do not know. A random variable is a measurable function Ω→X where Ω is the set of possible outcomes and X is a measurable space.

### What are random variables in terms of data science?

A random variable (also known as a stochastic variable) is **a real-valued function, whose domain is the entire sample space of an experiment**. ... Similarly, a random variable takes its domain (sample space of an experiment), processes it, and assigns every event/outcome a real value.

### What is random variable in ML?

A random variable is **the quantity produced by a random process**. A discrete random variable is a random variable that can have one of a finite set of specific outcomes. The two types of discrete random variables most commonly used in machine learning are binary and categorical.

### What are the similarities and differences of independent and dependent variables?

The independent and dependent variables are the two key variables in a science experiment. The independent variable is the one the experimenter controls. The dependent variable is the variable that changes in response to the independent variable. The two variables **may be related by cause and effect**.

### What are the types of discrete variables?

Discretely measured responses can be: **Nominal** (unordered) variables, e.g., gender, ethnic background, religious or political affiliation. Ordinal (ordered) variables, e.g., grade levels, income levels, school grades. Discrete interval variables with only a few values, e.g., number of times married.