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

Aggregaters, What Aggregate''s class III

What Aggregate''s class III

Requirements of good building stones , Requirements of Good Building Stones...

Requirements of Good Building Stones          Here described requirements of good building stones: Strength: The stone should be capable to resist the load coming on

Project planning, can you please provide with an example for mobilisation a...

can you please provide with an example for mobilisation and demobilisation plan, induction and deployment schedule, broad execution schedule in excel,quantity schedule for major qu

Dissimilarity in methods of compaction, Question Are there any dissimil...

Question Are there any dissimilarity in methods of compaction between clayey soil material and sandy material ? Answer The three key actions of compaction are static

Longitudinal steel – an enhancement of shear strength, Q. Longitudinal stee...

Q. Longitudinal steel – an enhancement of shear strength ? Furthermore to shear resistance provided by shear reinforcement, shear forces in a concrete section is also resisted

What is the long term effects - concrete, What is the Long Term Effects - C...

What is the Long Term Effects - Concrete Long term effects of  loads on structures consider all the effects including creep and shrinkage.

Surveying, describe two fundamentals purposes of surveying.

describe two fundamentals purposes of surveying.

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