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The joint p.d.f of a dimensional random variable (X,Y) is given by



f(x,y)=xy²+28, 0≤x≤2, Osys1 find (i) PX>1/Y<12 (ii) PY<12X>1.

Let X and Y be discrete random variable with probability function f (x, y)=x+y21, x=1, 2, 3 and y=1, 2. (i) Find the mean X and Y. (ii) Covariance of X, Y (iii) correlation of X and Y.

Explain how the presence of shield wires increases the power carrying



capacity of transmission lines.




A 100 MVA, 11 KV, 3-phase generator has a reactance of 20%. The generator



is connected to a 3-phase transformer T I rated 100 MVA, 11/132 KV with 10% reactance. The H.V. side of the transformer is connected to a transmission line of reactance 100 ohm. The far end of the line is connected to a step down three phase transformer T 2 rated 100MVA, 132/11 KV with 10% reactance. The generator supplies two motors connected in parallel on the L.V side of T 2 . The motors are rated at 25 MVA and 50 MVA both at 10 KV with 15% reactance. Taking the generator rating as base;



i) Draw a one-line and reactance diagrams representing the above



power system network showing all the values in per unit.



ii) Calculate the generator terminal voltage.




Explain the rationale for per unit system usage by electrical engineers.





With the help of phasor diagrams, discuss the relationship between the line-to-



line and line to-neutral voltages and currents for both wye and delta connected



systems.




Given a synchronous machine with three separate stator windings a, b, c



displaced physically by 120 o , sketch a graph showing the variations of emfs



developed in the windings against time.




What is the voltage transfer function of this buffer circuit?


 How is loss of prime mover detected? What are the problems encountered in implementing this protection?


Judge the feedback polarity and configuration of multistage amplifier in the circuit.

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