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

Levelling, how to establish temporary benchmark

how to establish temporary benchmark

Of obstacles to both chaining and ranging.., #questof obstacles to both cha...

#questof obstacles to both chaining and ranging. ion..

Shear moment diagram, how to draw shear moment diagram for cantileaver beam...

how to draw shear moment diagram for cantileaver beam

Open chanel flow, A rectangular channel is 3 m in width and draws water fro...

A rectangular channel is 3 m in width and draws water from a lake. The channel slope is 0.001 and the Manning’s n is 0.0013. What will be the discharge in the channel when the lake

Show the differences between GGBS and PFA, Q. Show the Differences Between ...

Q. Show the Differences Between GGBS and PFA? The use of GGBS as substitute of cement improves smaller reliance on PFA. Particularly GGBS is supposed to be more compatible with

State the term - failure due to strain, State the term - Failure Due to Str...

State the term - Failure Due to Strain In most of  the cases of pre-stressed concrete construction, the failure of underreinforced and lightly reinforced members shall take pla

Street originate in the plumbing term street ell, How did street originate ...

How did street originate in the plumbing term street ell? Ans) A "street ell" may have gotten its name due to it describes a 90° fitting particularly useful in tight, street dit

How do you determine specific gravity of cement, Cement is usually purchase...

Cement is usually purchased as a powdery substance that is mixed with sand, aggregate, gravel, and water to form concrete. As the cement itself is usually a powder, it is hard to c

Dock wall and dry dock, Dock Wall and Dry Dock: Dock Wall Fig...

Dock Wall and Dry Dock: Dock Wall Figure gives the diagram of a dock wall. Figure: Mass Concrete Dock Wall Dry Dock Figure 9 gives the details

Cement, Ask What is the density of cement?

Ask What is the density of cement?

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