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 negative skin friction, A square pile group of 16 piles passes ...

A square pile group of 16 piles passes by a filled up soil of 3 m depth. The pile diameter is 25 cm and pile spacing is 75 cm. If the unit cohesion of the material is 18 kN/m 2 an

Determine the governing effective length of a steel column, Determine the g...

Determine the governing effective length of a steel column? Determine the governing effective length of a W12 x 106 steel column that is 12' high, pinned at each end, and

LOADS, what are the difference between UDL and UVL?

what are the difference between UDL and UVL?

Key role of drilling fluid in rotary drilling, Question What is key rol...

Question What is key role of drilling fluid in rotary drilling in site search? Answer Drill fluid in rotating serves two main reasons. (i) Facilitate rotation of

Calculate the uniformly distributed load, Given: pretensioned rectangula...

Given: pretensioned rectangular beam b=6" h=20" f'c=4000psi f'ci=3000psi fti=.165ksi fts=.38ksi fci=1.8ksi fcs=1.8ksi R=0.80 Required: (a)Pi and e to maximize Md+

Void ratio, a soil sample is 38mm in diameter and 76mm and in its natural c...

a soil sample is 38mm in diameter and 76mm and in its natural condition weighs 168g.when dried completely in an oven weighs 13o.5g.the value of Gs is 2.73.what is the degree of sat

Revit , how to use the revit program

how to use the revit program

Fracking, cons and pros of fracking

cons and pros of fracking

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