 # What is variance and standard deviation of a discrete random variable?

## What is variance and standard deviation of a discrete random variable?

Definition 3.7. In words, the variance of a random variable is the average of the squared deviations of the random variable from its mean (expected value). The standard deviation is interpreted as a measure of how “spread out” the possible values of X are with respect to the mean of X, μ=E[X].

### What is a variance of a discrete random variable?

A measure of spread for a distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value. The variance of random variable X is often written as Var(X) or σ2 or σ2x.

How do you find the variance of discrete data?

Discrete variables Subtract the mean from each observation. Square each of the resulting observations. Add these squared results together. Divide this total by the number of observations (variance, S2).

Which of the following is an example of a discrete random variable?

If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor’s surgery, the number of defective light bulbs in a box of ten.

## How will you know that 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 discrete random variable X has a countable number of possible values. Example: Let X represent the sum of two dice.

### How do you find the variance of a discrete random variable?

For a discrete random variable X, the variance of X is obtained as follows: var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function pX(x) of X.

How do you find the variance of a continuous random variable?

These summary statistics have the same meaning for continuous random variables: The expected value µ = E(X) is a measure of location or central tendency. The standard deviation σ is a measure of the spread or scale. The variance σ2 = Var(X) is the square of the standard deviation.

How do you know if a random variable is discrete?

A discrete random variable has a countable number of possible values. The probability of each value of a discrete random variable is between 0 and 1, and the sum of all the probabilities is equal to 1. A continuous random variable takes on all the values in some interval of numbers.

## How do you calculate the variance of a random variable?

For a discrete random variable the variance is calculated by summing the product of the square of the difference between the value of the random variable and the expected value, and the associated probability of the value of the random variable, taken over all of the values of the random variable. In symbols, Var(X) = (x – µ) 2 P(X = x)

### What is the expected value for a random variable?

Definition (informal) The expected value of a random variable is the weighted average of the values that can take on, where each possible value is weighted by its respective probability.

What is the standard deviation of a discrete probability?

For a discrete random variable the standard deviation is calculated by summing the product of the square of the difference between the value of the random variable and the expected value , and the associated probability of the value of the random variable, taken over all of the values of the random variable, and finally taking the square root.

What is a variable variance?

Variance describes how much a random variable differs from its expected value. The variance is defined as the average of the squares of the differences between the individual (observed) and the expected value.