Univariate normal distribution, Civil Engineering

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

Posted Date: 1/30/2013 7:20:43 AM | Location : United States







Related Discussions:- Univariate normal distribution, Assignment Help, Ask Question on Univariate normal distribution, Get Answer, Expert's Help, Univariate normal distribution Discussions

Write discussion on Univariate normal distribution
Your posts are moderated
Related Questions
A soft, normally consolidated clay layer is 18 m thick. The natural water content is 45%. The saturated unit weight is 18 kN/m 3 ; the grain specific gravity is 2.70 and the liqui

long span bridge or continuous bridge which is more preferable and why ??? what is the major problem in continuous bridge and what would be its effect if there is any differential

Define Pneumatic Tools for Underwater Inspection of Bridge? These are more efficient than hand tools and cause less diver fatigue. The disadvantages are that below about 20 m,

Define the Shock Transmission Unit? Ever since engineers have started designing multi span simply supported bridges, they have been dreaming of connecting all the spans togethe

Q. How can a temporary diversion to laid a cross flowing river in case of disruption to rail traffic over a major bridge lasting over 6 months. Ans.- Temporary diversion


Hello I have an assignment due feb 1st at 3 pm. I wanted to know if it was possible that it gets solved



The two plates shown below are each 10-in. wide by ¾- in. thick. The gage distance, g, and the longitudinal spacing on each member is set at 4-in. Determine the axial strength of t