Education homework help. Q. A digital logic circuit is vulnerable to hardware faults at different test points. Suppose there are total N test points of which K (? N) are faulty.a. If an engineer selects n (? N) distinct points for testing. What is the probability that k (? n) are faulty points. Begin by defining X be random variable whose value equals number of k faults out of n test points.b. In Very Large Scale Integration (VLSI) the circuit size (therefore N) can be extremely large. Show how does the random variable X defined in (a) converge to a famous discrete random variable with parameters (n, p, k) where p = K/N.c. In modern VLSI circuits, the technological advancements render hardware faults very rare. Consequently, the average number of faults w in an N-test points VLSIcircuit can be considered constant. Under this assumption, show that in the circuit, that number of fault points designated by the random variable Z, converge from Yin (b) to Poisson random variable with w = K . Write down an expression for P(Z> k) in terms of k and w .d. Intel has developed an automatic system for testing hardware faults. The system spends t ms scanning a test point. If the last fault point was detected 1 ms ago,what is the probability that next fault point will be identified before 2 ms?

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