Question

Variance of n observations from normal distribution

Answer 1

Answer:

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

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Answer 2

, Xn are observations of a random sample of size n from the normal distribution N(μ, σ2) ¯X=1nn∑i=1Xi X ¯ = 1 n ∑ i = 1 n X i is the sample mean of the n observations, and. S2=1n−1n∑i=1(Xi−¯X)2 S 2 = 1 n − 1 ∑ i = 1 n ( X i − X ¯ ) 2 is the sample variance of the n observations.