Table of Contents

## What is random variable X?

A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.

### What is X in discrete random variable?

Means and Variances of Random Variables: The mean of a discrete random variable, X, is its weighted average. Each value of X is weighted by its probability. To find the mean of X, multiply each value of X by its probability, then add all the products.

#### How do you determine whether the random variable X has a binomial distribution?

You can identify a random variable as being binomial if the following four conditions are met:

- There are a fixed number of trials (n).
- Each trial has two possible outcomes: success or failure.
- The probability of success (call it p) is the same for each trial.

**What is binomial setting?**

The binomial setting consists of an experiment with observations satisfying: Each observation falls into one of just two categories, which for convenience we call “success” and “failure.” 4. The probability of a success, call it p, is the same for each observation. Definition.

**How do you know if a experiment is binomial?**

Criteria for a Binomial Probability Experiment

- A fixed number of trials.
- Each trial is independent of the others.
- There are only two outcomes.
- The probability of each outcome remains constant from trial to trial.

## What is a random variable?

Random Variable | Definition, Types, Formula & Example A random variable is a rule that assigns a numerical value to each outcome in a sample space. It may be either discrete or continuous. Visit BYJU’S to learn more about its types and formulas.

### Is a random variable discrete or continuous?

A random variable is said to be discrete if it assumes only specified values in an interval. Otherwise, it is continuous. We generally denote the random variables with capital letters such as X and Y.

#### What is the cumulative distribution function for a random variable?

All random variables (discrete and continuous) have a cumulative distribution function. It is a function giving the probability that the random variable Xis less than or equal to x, for every value x. For a discrete random variable, the cumulative distribution function is found by summing up the probabilities.

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

The formula for the variance of a random variable is given by; Var(X) = σ 2 = E(X 2) – [E(X)] 2. where E(X 2) = ∑X 2 P and E(X) = ∑ XP. Functions of Random Variables. Let the random variable X assume the values x 1, x 2, …with corresponding probability P (x 1), P (x 2),… then the expected value of the random variable is given by: