Univariate normal distribution, Civil Engineering

Assignment Help:

Univariate normal distribution:

Let X = (XI, X2, ..., Xn,) has the multivariate normal distribution (5.26) of Section 5.4. Show that Y = a X ' follows a univariate normal distribution where a = ( a1 a2 ..., an, ). Also find the mean and the variance of Y.

Solution:

We have

My(t)= E (etY)= E(etaX') = E(eτX')

where τ = ta = (ta1, ta2,..., tan ).

From Example 3 of Section 5.4, we have

MX (t) = E(e tX') = e τμ' +1/2(t∑ t')

Hence

My(t) = MX(τ) = eτμ' - ½ (τ∑τ') =e t(a μ')-1/2 t2(a∑a')

=e -1/2 t2 σ2

Where

1083_Univariate normal distribution.png

842_Univariate normal distribution3.png

Hence

MX(t) = e tμ+1/2 (t2σ2)

in other words Y - N ( μ, σ2 ) where

682_Univariate normal distribution2.png

842_Univariate normal distribution3.png


Related Discussions:- Univariate normal distribution

Distomat, applications of distomat in briefly

applications of distomat in briefly

Doors, types of doors with there prices

types of doors with there prices

Angular messurement using total stations, write a short note on angular mes...

write a short note on angular messurement using stations?

What is rapid sand filter, Q. What is Rapid Sand Filter? A Rapid Sand F...

Q. What is Rapid Sand Filter? A Rapid Sand Filter is a water treatment plant that includes provision for pre treating the water by coagulation and sedimentation for settlement

Soil particles for geotechnical design, Question Will it worthwhile to ...

Question Will it worthwhile to take out tests on particle density of soil particles for geotechnical design? Answer Particle density of soils is definite by ratio of

Casing has to be left in for mini-piles, Question What are thought in d...

Question What are thought in determining whether casings have to be left in for mini-piles ? Answer Contrary to most of pile design, design of min-piles is controlled

Why we need a high strength concrete in prestressing, Why we need a high st...

Why we need a high strength concrete in prestressing There is another aspect to why we need a high strength concrete in prestressing. Prestressed concrete is subjected to high

Total station, describe in detail the various parts of a total station

describe in detail the various parts of a total station

Project management, know the planking and strutting for shallow excavation...

know the planking and strutting for shallow excavation

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd