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
how to calculate various quantities of materials for wet mix macadam and dense bitumen macadam
Calculate the Horizontal Distance A surveyor's total station measured slope distance near station 3245+26.35 is recorded as 437.380-m with a zenith angle of 118º 48' 07" and a
Calculate Equivalent Uniform Annual Cost for the Excavator An earthwork contractor is considering the purchase of a new excavator. Based on 10% interest, the equivalent unifor
Determine the types of untensioned Reinforcement Reinforcement used as untensioned steel should be one of the following types : (a) Mild steel and medium tensile steel bar
A circular footing rests on a pure clay with qu = 270 kN/m 2 , at a depth of 1.8 m. Verify the diameter of the footing if it has to transmit a load of 720 kN. Suppose the bulk u
shear force ?
Explain Detention or Retention Ponds Detention/Retention Ponds: Designed to reduce and contain the peak runoff from developed areas (more impervious). Attempt to limit the runo
planking and strutting
The trigonometric levelling from the surveyor's notes is shown below. The ground elevation of T (ft) is most nearly: Solution: The elevation of point P can be found from: E
The soil in a borrow pit has a void ratio of 0.90. A fill-in-place volume of 20,000 m 3 is to be constructed with an in-place dry density of 18.84 kN/m 3 . If the owner of borr
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