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 I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 1 Time Series.
 2 Classical statistics.
 3 Bayesian statistics.
 A. Basic idea of Bayesian analysis.
 B. Estimating the mean of normal distribution with known variance.
 C. Estimating unknown parameters of normal distribution.
 D. Hierarchical analysis of normal model with known variance.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Estimating the mean of normal distribution with known variance.

e are given a sample from , where the is an unknown random variable. We will be following the outline of the section ( Basic idea of Bayesian analysis ). Our prior knowledge about the random variable is given by the normal distribution with some known parameters and . We proceed according to the ( Bayesian technique ) with the components and set according to the expressions We drop the normalization constants from our computation and write

 (Known Variance1)
We aim to put the term in the brackets into the form independent of terms. The independent terms would be dropped from the calculation because they belong to the normalization constant. We would consequently conclude that . We simplify by keeping only the -dependent terms: Hence, is a normal random variable of the form
 (Known Variance2)
where , is . We see that the distribution converges around and gradually forgets the parameters of the prior distribution.

 Notation. Index. Contents.