Make sure your work is genuine!

1.What are mutually exclusive events?

2.Give an example of a density function that is a standard probability that is applicable to discrete random variables.

3.Evaluate xy where a and b are complex cube roots and y=2a+7b and x=7a+2b.

4.Given state equations dx/dt=-2x+2u and y(t) = 0.5x, determine the transfer functionY(s)/U(s) of the system.

5.Give a representation L1= {x *|x contains even no's of 0's}, L2= {x *|x contains odd no's of 1's} determine the number of final stages in the language L1 U L2 .

6.Describe the number of tuples that are present in the finite state machine.

7.On which version was the unique identifier of the X.509 certificates added?

8.Which cryptographic algorithm is recommended by the X.509 certificate?

9.Determine the characteristic that is with the equation x^3+ax+b=0 in singular elliptic curve.

10. Determine the number of real and imaginary roots that are in the equation y2=x3-1.