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

Determine condition of activity in the network flow diagram, Determine the ...

Determine the condition of each activity in the network flow diagram shown below   Ans: a. Activity C can be started only after the completion of activities A and

State an expression for zero air-void line, State an expression for 'zero a...

State an expression for 'zero air-void line' and illustrate the line for a specific gravity of 2.65. What are the various factors that affect the compaction of soil in the field

Explain the suppressed rectangular weir, Explain the Suppressed Rectangular...

Explain the Suppressed Rectangular Weir If the length of the weir (b) equals the width of the channel, i.e., the flow is not "contracted".

Poly tetra fluoro ethylene, Question Why Poly tetra fluoro ethylene (PTFE...

Question Why Poly tetra fluoro ethylene (PTFE) is usually used in sliding bearings? Answer The choice of sliding surface of bearings is of very important importance since slid

Flow diagram of wet process, what type of basin in which is stored and wha...

what type of basin in which is stored and what is silos what is channel and correcting basins what type of clinker is formed

Surveying, what is meant by geodetic survey

what is meant by geodetic survey

Find the normal stress, Find the normal stress: Figure 1 shows the pro...

Find the normal stress: Figure 1 shows the projection of a rectangular prism ABCD, formed by adhesive bonding of two triangular prisms ABC and ACD. The state of stress in the

Determine the magnetic declination at a place, Example : Determine th...

Example : Determine the declination at a place, if at noon the magnetic bearing to the sun is (a) 358° (b) 185° Solution: (a) Referring to given figure (a) since the ma

Concrete , advantage and disadvantage of concrete

advantage and disadvantage of concrete

Permissible bearing pressure on poly tetra fluoro ethylene, Define Permissi...

Define Permissible Bearing Pressure on poly tetra fluoro ethylene? For the purpose of design, it is important to lay down permissible bearing pressure on PTFE sliding surfaces.

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