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

Abrassion test., abrasion test is conducted to find what

abrasion test is conducted to find what

What is shock transmission unit in bridges, Q. What is Shock transmission u...

Q. What is Shock transmission unit in bridges? Shock transmission unit is fundamentally a device connecting separate structural units. It's characterized by its ability to tran

Explain about noise absorptive materials, Q. Explain about Noise absorptive...

Q. Explain about Noise absorptive materials? The fundamental mechanism of noise absorptive material is to change the acoustic energy into heat energy. Amount of heat produced i

Hydraulics, The atmospheric pressure is given 680 mm Hg at a certain mounta...

The atmospheric pressure is given 680 mm Hg at a certain mountain location of elevation 2000 m. air density is 1.007 kg/m3. Find the pressure in kPa.

Show the properties of elastomer, Q. Show the Properties of Elastomer ? ...

Q. Show the Properties of Elastomer ? Though elastomeric bearings offer a number of advantages as compared to steel bearings, many failures have been reported pertaining to the

Sir I want to do assignments, sir I want to do assignments which were provi...

sir I want to do assignments which were provided by you sir could you please check with that

Explain the term - prestressing force, Explain the term - Prestressing Forc...

Explain the term - Prestressing Force Due to the stretching of  tendons, tensile stresses develop inside tendons. Resultant prestressing force in tendons may be calculated by m

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

Priciples of working from whole to part in surveying, What are the principl...

What are the principles of working from whole to part in surveying?

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