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, The obstacles that the students of civil engineering face when ...

The obstacles that the students of civil engineering face when it comes to produce a good piece of writing in English

Fly levelling, we are given a project on field.i''d like to know about how...

we are given a project on field.i''d like to know about how to start n proceed vd fly levelling in the field

Classification of bricks, Bricks may be broadly classified as following: ...

Bricks may be broadly classified as following: Paving bricks Building bricks Special bricks A.   Fire bricks B.   Building Bricks: These bricks are utilized fo

Flat footed rail, pls tell about flat footed rail and it weight how much fo...

pls tell about flat footed rail and it weight how much for 40 * 80 *10 mm

Energy equation, find the pressure head at 2-2 if the rate of flow in pipe ...

find the pressure head at 2-2 if the rate of flow in pipe is 0.36m^3/s

Home, Ask question #Mindasfimum 100 words accepted#

Ask question #Mindasfimum 100 words accepted#

Advantages of unbonded post-tensioning systems, Advantages of unbonded post...

Advantages of unbonded post-tensioning systems Similarly, some advantages of unbonded post-tensioning systems over bonded post-tensioning ones may be written as under :  (a)

Describe types of spurs, Q. Describe types of Spurs? Spurs can be of va...

Q. Describe types of Spurs? Spurs can be of varied types. They may be either permeable or impermeable. Permeable spurs are open structures constructed by driving wooden balties

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