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

Determine the soil shrinkage, Soil at a borrow area has a total unit weight...

Soil at a borrow area has a total unit weight of 120-PCF and a water content of 15 percent.  The soil from the borrow area will be used as structural fill and compacted to an avera

Between capping beams and ground beams for piles, Question What is majo...

Question What is major disparity between capping beams and ground beams for piles? Answer Capping beams for piles plan to transferring loads from directly spaced c

Concreting, #question why cracks develops on the surface of concrete on the...

#question why cracks develops on the surface of concrete on the next day of casting?

Stress corrosion of pre-stressing steel, Stress corrosion of pre-stressing ...

Stress corrosion of pre-stressing steel Stress corrosion is crystalline cracking of metals under tensile stresses in the presence of corrosive agents. Conditions for stress cor

Concrete mixers, what do you mean by buttering mixers

what do you mean by buttering mixers

Pumps, largest centrifugal pumps

largest centrifugal pumps

Water control for sheet pile walls, Q. Water control for sheet pile walls? ...

Q. Water control for sheet pile walls? Ground water flow into excavations constructed by sheet pile walls must be minimized in order to save the cost of the provision of pumpin

Calculate the tension force in sling - lifting load, Calculate the Tension ...

Calculate the Tension Force in Sling The rigging configuration shown below will be used to lift a bridge girder using a 200-ton capacity luffing jib crane onto the foundation a

Surveing, what is importance of positioning in different types of engineeri...

what is importance of positioning in different types of engineering?

Segmentally lined and sprayed concrete linings tunnels, Q. Segmentally line...

Q. Segmentally lined and Sprayed Concrete Linings tunnels? The fundamental difference between segmentally lined tunnels and SCL tunnels is that the sprayed concrete in SCL tunn

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