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 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

Bearing capacity, which kind of pile can increase the bearing capacity, if ...

which kind of pile can increase the bearing capacity, if the water level high in sang soil surface?

Plane table surveing, in plane table surveying which activity is done first...

in plane table surveying which activity is done first whether centering or levelling?

Surveying, describe two fundamentals purposes of surveying.

describe two fundamentals purposes of surveying.

Define recommendations for ptfe, Define Recommendations for PTFE? (a) I...

Define Recommendations for PTFE? (a) It can be either of the two forms given below: (i) Dimpled large sheet It may be circular or rectangular divided maximum into four pa

Shear force and bending moment, how to draw load intensity and bending mome...

how to draw load intensity and bending moment diagram form a given shear force diagram

Premix, how we can do good premix

how we can do good premix

Scale., how many scale are there and what are they use

how many scale are there and what are they use

Concrete carriageway comparatively, Question Why is slump specified in ...

Question Why is slump specified in concrete carriageway comparatively low like 30mmwhen compared with normal concrete like 75mm? Answer Slump of concrete carriageway

Syphon, what is the design of syphon

what is the design of syphon

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