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

STRUCTURAL MECHANICS, Define and explain Mohr’s theorem for finding slope a...

Define and explain Mohr’s theorem for finding slope and deflection.

Define channel jig, Define Channel Jig a) A channel jig is the simplest...

Define Channel Jig a) A channel jig is the simplest form of box jig. b) The work is placed in a channel shaped trough and clamped by mean of screw. c) It is utilized

AERATED CONCRETE, AIR ENTRAINING AGENT USED IN CONCRETE OTHER THAN ALUMINIU...

AIR ENTRAINING AGENT USED IN CONCRETE OTHER THAN ALUMINIUM POWDER

Determine the time of settlement of a sand particle, Using Stokes' law, det...

Using Stokes' law, determine the time of settlement of a sand particle of 0.2 mm size (specific gravity 2.67) through a depth of water of 30 cm. The viscosity of water is 0.001 N-s

Surveying, Distance ABC was measured with a 30m. Chain tested and found to ...

Distance ABC was measured with a 30m. Chain tested and found to be correct in the beginning of the work .after measuring AB=1.2 km chain was found to be 10 cm. To long chaining was

Design, what is the procedure to design the beam and column?

what is the procedure to design the beam and column?

Surveying, sample problems with solutions for probable value

sample problems with solutions for probable value

Show ph value of water, Q. PH Value of Water? It is a symbol for hydrog...

Q. PH Value of Water? It is a symbol for hydrogen ion concentration and indicates acidity or alkalinity. When P H Value more than 7 water is alkaline and less than 7 water is a

Pavement Drainage, What would be the best way to evaluate the field perform...

What would be the best way to evaluate the field performance benefits of subsurface drainage in a flexible pavement? Short term and long term, thick or thin HMA..

Define the marine growth - underwater inspection of bridges, Define the Mar...

Define the Marine Growth - Underwater inspection of bridges? Bridges on many inland waterways are relatively clean and free of marine growth. However, there is likelihood of ma

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