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

Simple bending, In case of simple bending after simply supported beam, deri...

In case of simple bending after simply supported beam, derive that M/I = s /y = E/R.

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

Define underwater inspection of steel or cast iron structure, Define Underw...

Define Underwater Inspection of steel or cast iron structures? Underwater Inspection of steel/cast iron structures may be carried out as under: i. Start the inspection at sp

Determine the allowable pressue, The data profile as shown in Figure is obt...

The data profile as shown in Figure is obtained. A best average of N values gave N 10 = 21, column loads including dead and live loads ranged from 500 kN to 950 kN. Determine the

What is admixtures, Q. What is Admixtures? These are the substance whic...

Q. What is Admixtures? These are the substance which are added to the concrete to improve its qualities either its placing or in its subsequent performance. An admixture may be

Rectangular tie, how to perform a rectangular tie using optical square?

how to perform a rectangular tie using optical square?

Alluvial streams, Alluvial Streams: In alluvial streams, the regime w...

Alluvial Streams: In alluvial streams, the regime width of a river is calculated from the Lacey's formula : W = 4.8 Q ½ where  W = Regime width in m, and Q = Discha

Explain the suppressed rectangular weir, Explain the Suppressed Rectangular...

Explain the Suppressed Rectangular Weir If the length of the weir (b) equals the width of the channel, i.e., the flow is not "contracted".

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