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Provide an argument as to why it is important to use the 4 dimensions for effecting discipline in Foundation Phase classrooms.
Let X1, X2 have the joint probability density function f(x1, x2) = 2e −(x1+x2) , 0 < x1, x2 < ∞ Let Y1 = X1, Y2 = X2 − X1.
(i) Using the change of variable technique, find the joint probability density function of Y1, Y2
(ii) Find the conditional distribution of Y2 given Y1
The joint probability density function of two random variables X1 and X2 is defined by f(x1, x2, x3) = 2, 0 < x1 < x2 < 1
Find the conditional distribution of X1 given X2 = x
Did good faith once again become a contractual requirement in South African law after the judgment in Everfresh Market Virginia (Pty) Ltd v Shoprite Checkers (Pty) Ltd 2012 (1) SA 256 (CC) was handed down? Explain your answer
The moment generating function of two jointly distributed random variables X1 and X2 is M(t1, t2) = e ^− 0.5 G where G = (7.51t 2 1 + 7.9t 2 2 + 3.8574t1t2 + 135.4t1 + 137.2t2) Using this function, find the correlation coefficient of of X1 and X2
A plate 60 mm wide and 12.5 mm thick is to be welded to another plate by means of parallel fillet welds. The plates are subjected to a load of 80 kN. Find the length of the weld. Assume allowable shear strength to be 60 MPa.
Let X and Y have joint probability distribution function f(x, y) = ( 2x+y /12) , (x, y) = (0, 1); (0, 2); (1, 2); (1, 3) 0, elsewhere
Find
(i) the covariance between X and Y.
(ii) the joint probability generating function of X and Y.
Given that y_1 = e^{x}
y1 =e^x
is a solution of xy’’+(1-2x)y’+(x-1)y=0
xy’’+(1−2x)y’+(x−1)y=0, find its second solution y_2
y2
(0,∞), which is linearly independent from y1
A double riveted lap joint is made between 15mm thick plates. The rivet diameter and pitch are 25 mm and 75 mm, respectively. If the ultimate stresses are 400 MPa in tension, 320 MPa in shear and 640 MPa in crushing, find the minimum force per pitch which will rupture the joint. If the above joint is subjected to a load such that the factor of safety is 4, find out the actual stresses developed in the plates and rivets.
Let X and Y be two independent random variables having joint probability density function f(x, y) = 1/ 2πσ2 e − (x−µ) 2 σ2 e − (y−µ) 2 σ2 − ∞ < x, y < ∞
Find the moment generating function of Z = X+Y 2 and hence the mean and variance of Z
#339914 on Dec 2023