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

.Chemestry, How desalination of water can be acheived by reverse osmosis an...

How desalination of water can be acheived by reverse osmosis and electrodialysis process?

Culverts, Can anyone help me in finding the formula for submerged and unsub...

Can anyone help me in finding the formula for submerged and unsubmerged flow in culverts?

Retaioning walls, what are the uses of retaining wall?!

what are the uses of retaining wall?!

Widening on curves, Widening on Curves: Pavements have to be widened ...

Widening on Curves: Pavements have to be widened on curves because of the fact that : (a) the vehicle has a wheel base and overhang on the front and rear, and the vehicle

Passenger conveyors, Passenger Conveyors: Passenger conveyors are used...

Passenger Conveyors: Passenger conveyors are used at locations where a large concentration of passengers has to be moved from one place to another. Escalators are used to conv

Calculate the uniform pressure on the soil, The plan of a proposed spoil he...

The plan of a proposed spoil heap is shown in Fig. The heap will stand on a thick deposit of soft clay with E-value 15 MN/m 2 . The uniform pressure on the soil may be suppose as 1

#title., what is the cause of scale and sludge formation and its diadvantag...

what is the cause of scale and sludge formation and its diadvantages

What do you mean by ggbs – cement replacement, Q. What do you mean by GGBS ...

Q. What do you mean by GGBS – cement replacement? From structural point of view GGBS replacement enhances higher durability, lower heat of hydration and higher resistance to su

What are basic types of elastomeric bearings, Q. What are basic types of el...

Q. What are basic types of elastomeric bearings? Three basic types of elastomeric bearings are used. 1. Plain elastomeric pads 2. Steel reinforced elastomeric pads 3.

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