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

State the method of pre- tensioning, State the method of Pre- Tensioning ...

State the method of Pre- Tensioning It is a method of prestressing concrete in which tendons are stretched or tensioned before concreting. In this form of construction, concr

How to determine the water content and bulk density, The wet weight of a sa...

The wet weight of a sample is missing in a Proctor test. The oven-dry weight of this sample is 189 N. The volume of the mould used is 1000 cm 3 . If the degree of saturation of

Calcculate the material costs, A capital improvement project requires the i...

A capital improvement project requires the installation of a property line fence along the 250-ft Northern boundary line.The decorative aluminum fence is constructed of posts space

Determine the preliminary settlement analysis, Preliminary settlement analy...

Preliminary settlement analysis for a building indicated a settlement of 50 mm in 4 years and an  ultimate  settlement  of  250 mm.  The average pressure increment in the clay stra

Structural analysis, steps to analysis a portal frame with sway condition

steps to analysis a portal frame with sway condition

Theodolite, convert whole circle bearing to reduce bearing formula

convert whole circle bearing to reduce bearing formula

Define the types of shock transmission unit, Define the Types of shock tran...

Define the Types of shock transmission unit? Presently two types of STUs are available in the overseas market: (a) Silicon putty based from UK and USA. (b) Oil based from

Size of drainage near roads, how to calculate the size of drainage(box) wid...

how to calculate the size of drainage(box) width and height?

Wet mix Macadam, Test required before laying or after laying.

Test required before laying or after laying.

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