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

Local scour at obstructions in rivers, Q. Local Scour at obstructions in ri...

Q. Local Scour at obstructions in rivers? When the water flow in river is deflected by obstructions such as bridge piers, scouring would occur arising from formation of vortexe

Inspection and testing, Q. Inspection and testing ? The inspection and ...

Q. Inspection and testing ? The inspection and tests on elastomer and the finished bearings are very important aspects of ensuring a satisfactory performance of the bearing. IR

Determine the flow rate if the pump is turned at 100 rpm, One pump lifts st...

One pump lifts storm water from a storage tunnel wet well a constant vertical distance of 150 ft. The equivalent length Le of the 14 in diameter piping is 1,000 ft. Pressure drop d

Soil structure, what is soil structure and types of soil structure?

what is soil structure and types of soil structure?

Explain critical factor in design of shock transmission unit, Explain Criti...

Explain Critical factor in Design of shock transmission unit? (a) STUs are unidirectional devices for load transmission. If out of plane forces will be acting on the STU, the a

BONDS, ADVANTAGE OF FLEMISH BOND

ADVANTAGE OF FLEMISH BOND

Calculate the principal stresses for the state of stress, Calculate the pri...

Calculate the principal stresses for the state of stress: Calculate the principal stresses and principal planes for the state of stress shown in Figure. Figure

Geotech, soil sample investigation

soil sample investigation

Usage of double air valves and single air valves, Question In designig ...

Question In designig of watermains, how to decide usage of double air valves and single air valves ? Answer Single air control device let squeezing air out of p

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