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 the unit weight of water, In a pipette analysis, 0.5 N of dry soil ...

In a pipette analysis, 0.5 N of dry soil (fine fraction) of specific gravity 2.72 were mixed in water to form half a litre of uniform suspension. A pipette of 10 ml capacity was

Analytical methods for pollutants under the clean water act, Analytical Met...

Analytical Methods for Pollutants Regulated Under the Clean Water Act? We suppose that you have knowledge of and access to the relevant analytical methods. These methods cover

Major considerations in selecting marine plants, Question What are majo...

Question What are major considerations in selecting marine plants and land plants for fitting of band drains? Answer For fitting of band drains by marine plants,

Defected Timber, Please tel me about Timber Defected

Please tel me about Timber Defected

DECK ENGINEERING CALCULATIONS, We need eng. calcs for a deck 17''x 10 feet...

We need eng. calcs for a deck 17''x 10 feet.attach to the guest house. calculations will be for 230 psi snow load . in the city of Mammoth lakes Ca. deck is supported for 3 girder

Mr Kamal Saxena, What is WBM road. How it is constructed?

What is WBM road. How it is constructed?

State the total rankine active thrust per metre run, A wall with a smooth v...

A wall with a smooth vertical back 9 m high ropes a purely cohesive soil with  c = 10 kN/m 2 and γ = 18 kN/m 3 . State the total Rankine active thrust per metre run, the positi

Tension members, Tension Members: You have learnt about the Standard s...

Tension Members: You have learnt about the Standard specification for structural steel and various types of structural steel rolled sections. Different types of loads, stresse

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