# Probability Assignment | Professional Writing Services

# Probability Assignment | Professional Writing Services

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 a random variable whose value equals a 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 wins an N-test points VLSI

circuit 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 Y

in (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 the next fault point will be identified before 2 ms?

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## Probability Assignment | Professional Writing Services

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**Probability Assignment | Professional Writing Services **

# Probability Assignment | Professional Writing Services

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 a random variable whose value equals a 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 wins an N-test points VLSI

circuit 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 Y

in (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 the next fault point will be identified before 2 ms?

Get Statistics homework help today

TOP ACADEMIC WRITER

He has decades of experience in the education field and has served in the examination boards of some of the top Universities within & outside the United States America.

## Probability Assignment | Professional Writing Services

**Probability Assignment | Professional Writing Services **