Normal distribution var(x)=sigma^2

Click For Summary
SUMMARY

The discussion centers on the relationship between variance and standard deviation in a normal distribution. It establishes that if a random variable X is normally distributed with mean μ and standard deviation σ, then the variance of X is defined as var(X) = σ². The definitions of variance and standard deviation are crucial to understanding this relationship, and the discussion emphasizes that this result follows directly from these definitions.

PREREQUISITES
  • Understanding of normal distribution concepts
  • Knowledge of statistical definitions of variance and standard deviation
  • Familiarity with mathematical notation and symbols
  • Basic probability theory
NEXT STEPS
  • Study the properties of normal distributions in depth
  • Learn about the Central Limit Theorem and its implications
  • Explore the calculation of variance and standard deviation in different distributions
  • Investigate the use of statistical software for variance analysis, such as R or Python's NumPy
USEFUL FOR

Students of statistics, data analysts, and anyone seeking to deepen their understanding of statistical concepts related to normal distributions and variance calculations.

badgerbadger
Messages
7
Reaction score
0
suppose that X is normally distributed with mean u and standard deviation sigma. show that var(x)=sigma^2.[you many use the fact that if Z is standard normally distributed, then EZ=0 and var(x)=1]
 
Physics news on Phys.org
Okay, what is the definition of "variance"? What is the definition of "standard deviation"? The result should be immediate from the definitions.
 

Similar threads

High School Variance & Standard Deviation
  • · Replies 42 ·
2
Replies
42
Views
5K
Graduate A different discrete normal distribution
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Citation needed: Only multivariate rotationally invariant distribution with iid components is a multivariate normal distribution
  • · Replies 3 ·
Replies
3
Views
2K
MHB How Do You Minimize Mean Square Deviation in Dice Roll Predictions?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Normality of errors and residuals in ordinary linear regression
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Combining model uncertainties with analytical uncertainties
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Why does normal distribution turn into t distribution when variance is unknown?
  • · Replies 5 ·
Replies
5
Views
5K
MHB Likelihood Ratio Test for Common Variance from Two Normal Distribution Samples
  • · Replies 1 ·
Replies
1
Views
4K
MHB Sampling Distribution of the Sample Means from an Infinite Population
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Can a Gaussian distribution be represented as a sum of Dirac Deltas?
  • · Replies 2 ·
Replies
2
Views
3K