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

Classification of timber based on durability, Classification Based on Durab...

Classification Based on Durability: Durability tests are conducted by the forest research establishment. They cover test specimen of size 600 × 50 × 50 mm in the ground to hal

On-line storage vs. off-line storage, On-line storage vs. off-line storage ...

On-line storage vs. off-line storage Design of storage pond is commonly divided into off -line storage and on-line storage. The on-line storage concept includes inclusion of s

#manholes, #how are manholes mantained

#how are manholes mantained

FOUNDATION, TYPE OF FOUNDATION IN LATERITE SOIL

TYPE OF FOUNDATION IN LATERITE SOIL

Glazed tiles for construction material, Q. Glazed tiles for Construction Ma...

Q. Glazed tiles for Construction Material? Glazed tiles are only meant for dadoes of bath room, Toilet and kitchens etc as they have no strength . Normally 8'' x 4'' g

Shear lag in typical box-girder bridge, Shear lag in typical box-girder bri...

Shear lag in typical box-girder bridge For multiple-cell box girders, there are normally two arrangements. First one is that independent cells are connected by their top flang

Determine the elastic settlement of a rectangular foundation, Determine the...

Determine the elastic settlement of a rectangular foundation, 6 m × 12 m, on a uniform sand with E = 20,000 kN/m 2 and Poisson's ratio,   = 0.2. The contact pressure is 200 kN/m 2

Introduction to engineering mechanics, Deternim the angle A for which the m...

Deternim the angle A for which the moment of the 500N force is maximum about a point o. also find the maximum momentum

Single flemish bond, advantages and disadvantages in single flemish bond

advantages and disadvantages in single flemish bond

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