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 modulus of elasticity, Classification Bas...

Classification Based on Modulus of Elasticity: Young's modulus is resolute by conducting bending test. On this basis timber is classified as following: Group A: E = 12.5 kN

Write short note on skv process of thermit welding, Q. Write short note on...

Q. Write short note on SKV  process of thermit welding? This term is used for welding by Alumino thermic process with short preheat time. The time required for preheat with pet

Define the meaning of tensile stresses, Tensile stresses It has been po...

Tensile stresses It has been possible to introduce tensile stresses of upto 850 N/mm 2 in tendons with the use of this method. But the method is not suited in situations where

Stone soling - road pavements, Stone Soling: One of the early practic...

Stone Soling: One of the early practices in road construction was to provide a stone soling 150-225 mm in thickness. The stones are laid by manual labour, and stone spalls ar

Explain the national primary drinking water standards, Explain the National...

Explain the National Primary Drinking Water Standards Safe Drinking Water Act (SDWA, 1974) required EPA to establish maximum contaminant levels (MCLs) for public water systems

Engineering mathamatics, #question.A strain gauge arrangement is used to me...

#question.A strain gauge arrangement is used to measure the applied force of a comnplex shaped civil engineering structure. Theoretical analysis have been round the relationship be

Major compensation of using hdpe as compared with cast iron, Question N...

Question Now, mainly flap valves are ended of HDPE. What is the major compensation of using HDPE as compared with cast iron? Answer (i) It has no response with sewage a

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