# How do you find the standard deviation of a uniform distribution?

## How do you find the standard deviation of a uniform distribution?

The variance of a continuous uniform distribution is Var(X)=(b−a)212 V a r ( X ) = ( b − a ) 2 12 , and the standard deviation is σ=√(b−a)212=b−a2√3 σ = ( b − a ) 2 12 = b − a 2 3 .

## What is the mean and variance of a uniform distribution?

The mean of the uniform distribution U(a,b) : μ = (a + b) / 2. The variance of the uniform distribution U(a,b) : σ² = (b – a)² / 12. As you’re well aware, the standard deviation is simply the square root of the variance, so you can easily transform one into the other.

How do you find the mean and standard deviation of a uniform distribution in R?

The Uniform Distribution in R

1. The mean of the distribution is μ = (a + b) / 2.
2. The variance of the distribution is σ2 = (b – a)2 / 12.
3. The standard deviation of the distribution is σ = √σ2

### Does uniform distribution have variance?

The uniform distribution is used to describe a situation where all possible outcomes of a random experiment are equally likely to occur. You can use the variance and standard deviation to measure the “spread” among the possible values of the probability distribution of a random variable.

### How do you derive the variance of a uniform distribution?

From the definition of the continuous uniform distribution, X has probability density function: fX(x)={1b−aa≤x≤b0otherwise. From Variance as Expectation of Square minus Square of Expectation: var(X)=∫∞−∞x2fX(x)dx−(E(X))2.

How do you find a and b in a uniform distribution?

The notation for the uniform distribution is X ~ U(a, b) where a = the lowest value of x and b = the highest value of x. The probability density function is f(x)=1b−a f ( x ) = 1 b − a for a ≤ x ≤ b.

#### What is the standard deviation of a uniform probability distribution?

Uniform Distribution

Mean (A + B)/2
Median (A + B)/2
Range B – A
Standard Deviation \sqrt{\frac{(B – A)^{2}} {12}}
Coefficient of Variation \frac{(B – A)} {\sqrt{3}(B + A)}

#### How do you find the standard deviation of a uniform distribution in Excel?

How to Use the Uniform Distribution in Excel

1. The mean of the distribution is μ = (a + b) / 2.
2. The variance of the distribution is σ2 = (b – a)2 / 12.
3. The standard deviation of the distribution is σ = √σ2

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

For a random variable following this distribution, the expected value is then m1 = (a + b)/2 and the variance is m2 − m12 = (b − a)2/12.

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