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

Minimum and maximum distance between bars, Q. Minimum and maximum distance ...

Q. Minimum and maximum distance between bars? Minimum distance between bars and maximum distance between bars In some codes, a minimum distance amid bars is specified to

Leveling, cooke''s reversable level

cooke''s reversable level

Explain basic need of design of shock transmission unit, Explain the Basic ...

Explain the Basic requirement of Design of shock transmission unit? The STU must withstand the specified design load. The stroke of the piston must be bigger than the movement

Process of installation of elastomeric bearing, The process of installation...

The process of installation of elastomeric bearing differs in case of precast vis-a-vis cast-in-situ girders. For precast girders, the bearing may be fixed to the underside of the

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

Water absorption test - tests on stones, Water Absorption Test: In t...

Water Absorption Test: In this test cube specimen weighing approximate 50 grams are prepared and the test is carried out in the steps following: 1.    Note down the weigh

What is the station at point b, What is the station at Point B? SO...

What is the station at Point B? SOLUTION 3 Station at Point A = Sta 22+45  Station at Point B = (Sta 22+45) + 1028' = 2245'+1028' =3273'  = Sta 32+73

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