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

Harbour, typical layout showing dock,quay.jetties,turning circle,pier

typical layout showing dock,quay.jetties,turning circle,pier

MatLab, can you help me with an assignment

can you help me with an assignment

Joints in box culverts and channels, Joints in box culverts and channels - ...

Joints in box culverts and channels - necessity of water tightness The joints for box culverts and channels must be capable of accommodating movements arising from moisture an

Determine the preliminary settlement analysis, Preliminary settlement analy...

Preliminary settlement analysis for a building indicated a settlement of 50 mm in 4 years and an  ultimate  settlement  of  250 mm.  The average pressure increment in the clay stra

Strength of materials, Didtribution of shear stree over a triangular sectio...

Didtribution of shear stree over a triangular section

Design the transverse reinforcement, Figures (a) and (b) respectively give ...

Figures (a) and (b) respectively give details of a simply-supported bridge beam and its (idealised) cross-section. In addition to the dead load of 25 kN/m (including self weight),

Define types of inspection of bridge, Define Types of Inspection of Bridge?...

Define Types of Inspection of Bridge? Underwater inspections are generally categorised into five types: - Inventory - Routine - Damage - In-depth - Interim

Calculates the energy required, Write a program called, A1Q1, that reads a ...

Write a program called, A1Q1, that reads a single letter.   It will then display the corresponding ASCII code of the letter and prints the next character and the character which is

State the term - relaxation of stress in steel, State the term - Relaxation...

State the term - Relaxation of Stress in Steel If we keep a high-tensile steel wire stretched and maintained at a constant strain, the value of the force in the wire does not

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