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

What do you mean by settlement cracks, Q. What do you mean by Settlement Cr...

Q. What do you mean by Settlement Cracks? Settlement cracks normally take place in diagonal position. Sometimes vertical cracks may also take place (Figure (a)). Settlement cra

Define the types of sedimentation, Define the Types of Sedimentation 1....

Define the Types of Sedimentation 1. Type I Particles that settle discretely (settle as individual particles) sand, grit Pre-sedimentation for sand prior to co

Hydraulics assignment , I have assignment for hydraulics can you help for t...

I have assignment for hydraulics can you help for that

Online job, I am M tech in civil engg looking for online assignment job.

I am M tech in civil engg looking for online assignment job.

Describe the terms inside clearance and outside clearance, a) Explain with ...

a) Explain with a neat sketch how will you carry out the wash boring method of soil exploration. What are its merits and demerits? b) Describe the terms 'inside clearance' and '

Whole base of mat, Question In modeling a nonrigid mat foundation by us...

Question In modeling a nonrigid mat foundation by using elastic springs, have a uniform modulus of subgrade reaction be used along whole base of mat ? Answer A bed of

Curved prestressed bridge, In a curved prestressed bridge , how ought to t...

In a curved prestressed bridge , how ought to the guided bearings in piers of curved region be oriented with respect to a fixed bearing in abutment?

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