Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
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 tμ -1/2 t2 σ2
Where
MX(t) = e tμ+1/2 (t2σ2)
in other words Y - N ( μ, σ2 ) where
Explain Fluid Mechanics or Properties – Viscosity A measure of a fluid's resistance to flow when acted upon by an external force such as pressure or gravity. Also termed, "Abso
Determine the head loss due to friction using the Darcy-Weisbach equation. The water is pumped at 3.0 gallons per minute, has a temperature of 60 °F and is pumped through a 1inch s
Explain RCRA and HSWA - Hazardous Waste Regulations 1. In 1976, Congress passed the Resource Conservation and Recovery Act (RCRA) and directed EPA to establish hazardous waste
Q. What are the various impurities in water? Ans.- Impurities in water - The impurities in water are classified as - i. Suspended Impurities. ii. Colloidal Impuritie
Q. Concrete cover to enhance fire resistance? In the event of exposing concrete structures to a fire, a temperature gradient is established across the cross section of concrete
Compute the safe bearing capacity of a square footing 1.5 m × 1.5 m, located at a depth of 1 m below the ground level in a soil of average density 20 kN/m 3 . = 20°, N c = 17.7,
Q. Explain the process of Directed Track Maintenance? DTM is a method to maintain the track is directed every day and not as a prescribed routine. DTM essentially consists of n
Explain the Limitations of Rebound Hammer? The following characteristics of concrete can affect the correlation of the rebound number with the actual surface hardness and shoul
Explain the Unconfined Aquifer Also termed "free aquifer". Groundwater flows by gravity from high head to low head. The upper water surface is termed "water table", is influenc
Q. Show Suspended Impurities in water? The solid particles which are dispersed in water are referred as suspended Impurities. These are microscopic as under-
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!
whatsapp: +91-977-207-8620
Phone: +91-977-207-8620
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd