An integrated circuit chip measuring 1 cm by 1 cm is manufac

An integrated circuit chip measuring 1 cm by 1 cm is manufactured on a fabrication line where defects
occur on wafers at the average rate of 1 defect per square centimeter.
(a) What is the probability that a randomly selected chip from the fabrication line chip will have no
flaw on it? If chips cost $10 each to make, but only chips without a flaw can be sold, what is the
average cost of producing marketable chips?
(b) Suppose now the chip has designed into it a built-in redundancy so that any single flaw on the chip
can be e?ectively repaired, but with this facility, the chip area is increased by 10%, and the cost
of producing the new chip is now $12. What is the probability that a randomly selected chip from
the fabrication facility would function? What would the average cost of manufacture of functioning
ICs now be?
Hint: For X ? P(?), P(X = k) = e

Solution

Let X: Number of defects/flaws occurred

It is given that defects can occur at an average rate of 1 defect per square centimetre

Here X will follow poisson distribution with m = 1.

Probability mass function for poisson distribution is given as follows:

P[ X= k] = ( e^-m * m^k)/ k! , k=0,1,2,3,