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

Assignment, on timber, varieties , preservation, and seasoning of timber

on timber, varieties , preservation, and seasoning of timber

Explain about bentonite slurry and polymeric slurry, Q. Explain about Bento...

Q. Explain about Bentonite slurry and polymeric slurry? For the construction of diaphragm walls, bentonite slurry is generally used to form a filter cake on walls of trenches t

Explain the tertiary treatment for wastewater, Explain the Tertiary Treatme...

Explain the Tertiary Treatment for Wastewater Tertiary Treatment: in cases where secondary treatment is not adequate (particularly if the discharges are into a sensitive water

Deep foundation, At what places deep foundation are made?

At what places deep foundation are made?

Strain due to bending, Beam of arbitrary cross-sectionsubjected to couples ...

Beam of arbitrary cross-sectionsubjected to couples M Bending moment at any sectionis M Consider segment of beam subtended by angle θ Some fibres will shorten e.g. ABand o

Manhole covers finished of cast iron same as ductile iron, Question Why are...

Question Why are manhole covers finished of cast iron as same are through of ductile iron ? Answer Usually, manholes covers are made of cast iron. Though, in viewpoint of pipe

What is material at site return, Q. What is Material at site Return? Th...

Q. What is Material at site Return? The authority is executive charge of a work should be responsible for holding in safe custody for controlling the consumption and to the ext

Surveying, 3 types of obstacles in chaining detail

3 types of obstacles in chaining detail

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