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Nth Moment of Discrete Random Variable Formula

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Nth Moment of Discrete Random Variable represents the nth moment of the random variable r, which typically refers to the intensity level of a pixel in the image. Check FAQs

μ n = \sum (x, 0, L - 1, p ri \cdot {(r i - m)}^{n})

μ_n - Nth Moment of Discrete Random Variable?L - Number of Intensity Levels?p_ri - Probability of Intensity Ri?r_i - Pixel Intensity Level?m - Mean of Intensity Level?n - Order of Moment?

Nth Moment of Discrete Random Variable Example

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Here is how the Nth Moment of Discrete Random Variable equation looks like with Values.

Here is how the Nth Moment of Discrete Random Variable equation looks like with Units.

Here is how the Nth Moment of Discrete Random Variable equation looks like.

3276.8 = \sum (x, 0, 4 - 1, 0.2 \cdot {(15 - 7)}^{4})

3276.8W/m² = \sum (x, 0, 4 - 1, 0.2 \cdot {(15W/m² - 7)}^{4})

3276.8 = \sum (x, 0, 4 - 1, 0.2 \cdot {(15 - 7)}^{4})

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Nth Moment of Discrete Random Variable Solution

Follow our step by step solution on how to calculate Nth Moment of Discrete Random Variable?

FIRST Step Consider the formula

μ n = \sum (x, 0, L - 1, p ri \cdot {(r i - m)}^{n})

Next Step Substitute values of Variables

∴

μ n = \sum (x, 0, 4 - 1, 0.2 \cdot {(15W/m² - 7)}^{4})

Next Step Prepare to Evaluate

∴

μ n = \sum (x, 0, 4 - 1, 0.2 \cdot {(15 - 7)}^{4})

LAST Step Evaluate

∴

μ n = 3276.8W/m²

Nth Moment of Discrete Random Variable Formula Elements

Variables

Functions

Nth Moment of Discrete Random Variable

Nth Moment of Discrete Random Variable represents the nth moment of the random variable r, which typically refers to the intensity level of a pixel in the image.

Symbol: μ_n

Measurement: IntensityUnit: W/m²

Note: Value should be greater than 0.

Formulas to find Nth Moment of Discrete Random Variable

Number of Intensity Levels

Number of Intensity Levels is the total number of distinct intensity values an image can represent, determined by its bit depth.

Symbol: L

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Intensity Levels

Probability of Intensity Ri

Probability of Intensity Ri represents the probability of occurrence of the intensity level r_i. It indicates the likelihood of encountering a pixel with that specific intensity value in the image.

Symbol: p_ri

Measurement: NAUnit: Unitless

Note: Value should be less than 1.1.

Formulas to find Probability of Intensity Ri

Pixel Intensity Level

Pixel Intensity Level refer to the range of possible intensity values that can be assigned to pixels in an image. This concept is particularly relevant in grayscale images.

Symbol: r_i

Measurement: IntensityUnit: W/m²

Note: Value should be greater than 0.

Formulas to find Pixel Intensity Level

Mean of Intensity Level

Mean of Intensity Level represents the mean of the intensity levels, which is essentially the average intensity value across the entire image.

Symbol: m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Mean of Intensity Level

Order of Moment

Order of Moment denotes the order of the moment, which determines the weighting applied to each intensity level.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than -0.1.

Formulas to find Order of Moment

sum

Summation or sigma (∑) notation is a method used to write out a long sum in a concise way.

Syntax: sum(i, from, to, expr)

Other formulas in Intensity Transformation category

Go Wavelength of Light

W = \frac{[c]}{v}

Go Number of Intensity Levels

L = 2^{n b}

Go Bits Required to Store Digitized Image

n id = M \cdot N \cdot n b

Go Bits Required to Store Square Image

b s = {(N)}^{2} \cdot n b

How to Evaluate Nth Moment of Discrete Random Variable?

Nth Moment of Discrete Random Variable evaluator uses Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment) to evaluate the Nth Moment of Discrete Random Variable, The Nth Moment of Discrete Random Variable formula characterizes the average behavior of pixel intensity (r) raised to the power of n in a digital image. Nth Moment of Discrete Random Variable is denoted by μ_n symbol.

How to evaluate Nth Moment of Discrete Random Variable using this online evaluator? To use this online evaluator for Nth Moment of Discrete Random Variable, enter Number of Intensity Levels (L), Probability of Intensity Ri (p_ri), Pixel Intensity Level (r_i), Mean of Intensity Level (m) & Order of Moment (n) and hit the calculate button.

FAQs on Nth Moment of Discrete Random Variable

What is the formula to find Nth Moment of Discrete Random Variable?

The formula of Nth Moment of Discrete Random Variable is expressed as Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment). Here is an example- 3276.8 = sum(x,0,4-1,0.2*(15-7)^4).

How to calculate Nth Moment of Discrete Random Variable?

With Number of Intensity Levels (L), Probability of Intensity Ri (p_ri), Pixel Intensity Level (r_i), Mean of Intensity Level (m) & Order of Moment (n) we can find Nth Moment of Discrete Random Variable using the formula - Nth Moment of Discrete Random Variable = sum(x,0,Number of Intensity Levels-1,Probability of Intensity Ri*(Pixel Intensity Level-Mean of Intensity Level)^Order of Moment). This formula also uses Summation Notation (sum) function(s).

Can the Nth Moment of Discrete Random Variable be negative?

No, the Nth Moment of Discrete Random Variable, measured in Intensity cannot be negative.

Which unit is used to measure Nth Moment of Discrete Random Variable?

Nth Moment of Discrete Random Variable is usually measured using the Watt per Square Meter[W/m²] for Intensity. Watt per Square Centimeter[W/m²], Watt per Square Millimeter[W/m²], Kilowatt per Square Meter[W/m²] are the few other units in which Nth Moment of Discrete Random Variable can be measured.

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Nth Moment of Discrete Random Variable Formula

Nth Moment of Discrete Random Variable Example

Nth Moment of Discrete Random Variable Solution

Nth Moment of Discrete Random Variable Formula Elements

Other formulas in Intensity Transformation category

How to Evaluate Nth Moment of Discrete Random Variable?

FAQs on Nth Moment of Discrete Random Variable

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