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

Project data , finding the mean ,mode and mediam

finding the mean ,mode and mediam

Role of rebate in typical construction joint, Question What is role of reba...

Question What is role of rebate in typical construction joint ? Answer Construction joints are formed on sites to facilitate construction procedure. Though, if improperly constr

What is thermo-electric prestressing, What is Thermo-electric prestressing ...

What is Thermo-electric prestressing We know that, stretched tendons are used in prestressed concrete. Stretching of tendons may be accomplished by using jacks or by other mea

Erosion ocntrol, java program to design a SD-3 sediment pond per Georgia er...

java program to design a SD-3 sediment pond per Georgia erosion control manual

Inspection of girder bridge, Q. As an AEN in charge, what inspection will...

Q. As an AEN in charge, what inspection will you under taken at the time of inspection of Girder Bridge 3 x 60 feet. Please explain the important items to be o

What is the pre-tensioned concrete, What is the Pre-tensioned concrete ...

What is the Pre-tensioned concrete In Pre-tensioned concrete tendons are kept stretched with suitable mechanisms and concrete is cast into the forms through which stretched ten

Calculate the hydrostatic force, The steel oil container shown in the figur...

The steel oil container shown in the figure has a circular lid centred on its sloping wall. The lid is hinged at A and held closed with a frictionless stopper at B. The lid is made

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