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

Components of a typical expansion joint, Question Explain components of a t...

Question Explain components of a typical expansion joint? Answer Dowel bar-This is major component of joint. It serves to guide direction of movement of concrete growth. Therefo

Landslides induced by rainfall, Landslides induced by rainfall After r...

Landslides induced by rainfall After rainfall, groundwater pressure is built up and this elevates ground water table. Water inside the pores of soil reducesthe effective stres

Foundations, Design a footing of a bridge pier

Design a footing of a bridge pier

Define mechanical tool for underwater inspection of bridge, Define Mechanic...

Define Mechanical tool for underwater inspection of bridge? Mechanical devices that involves a Schmidt Test Hammer for computing concrete surface hardness, and rotary coring eq

Surveying, earthen dam and gravity dam

earthen dam and gravity dam

Marked., who invented the first LA abrasion test machine

who invented the first LA abrasion test machine

AUTOCAD, do you people deal with autocad

do you people deal with autocad

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