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

Design the drainage pipes system in reclamation areas, Q. Design the Draina...

Q. Design the Drainage pipes system in reclamation areas? In reclamation areas drainage pipes are generally laid at flatter gradients when compared with upstream stormwater pip

Construction - concrete pavement, Construction: Construction is usual...

Construction: Construction is usually done by one of the three methods: (a) Manual method, providing steel or wooden forms, pouring concrete and compacting by means of nee

Hydraulics, A tank with vertical sides contain 3m of water in the bottom, o...

A tank with vertical sides contain 3m of water in the bottom, overlain by 4m of oil with no intermixing. Draw pressure diagram due to the oil and water on one of the tank sides and

Material engineering assignment, select three materials metal and non meala...

select three materials metal and non mealat at least one of the selected materials shold change its property

Explain the traffic safety - transportation, Explain the Traffic Safety - T...

Explain the Traffic Safety - Transportation Crash rates are normally considered better indicators of risk than crash frequencies.  a. Crash rates for intersections are norma

Trigo, A pole which leans 11o from the vertical toward the sun casts a shad...

A pole which leans 11o from the vertical toward the sun casts a shadow 12m long when the angle of elevation of the sun is 40o. Find the length of the pole

Effect of concrete placing temperature, Effect of concrete placing temperat...

Effect of concrete placing temperature on early thermal movement Rate of hydration of cement paste is related to placing temperature of concrete. Rate of heat production is giv

Explain the toxic characteristics - hazardous waste, Explain the Toxic Char...

Explain the Toxic Characteristics - Hazardous Waste - From the results of either  - Extraction Procedure(EP) toxicity (prior to March 1990) or Toxicity Characteristic Leachi

Timber, defects in timber?

defects in timber?

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