In a semiconductor manufacturing process, three wafers from a lot are tested. each wafer is classified as pass or fail. assume that the probability that a wafer passes the test is 0.6 and that wafers are independent. determine the cumulative distribution function of the number of wafers from a lot that pass the test at specified values. round your answers to three decimal places (e. g. 98.765).

F(x) = 0           ;  x < 0

         0.064   ;  0 ≤ x < 1

         0.352   ;  1 ≤ x < 2

         0.784   ;  2 ≤ x < 3

            1        ;    x ≥ 3

Explanation:

Each wafer is classified as pass or fail.

The wafers are independent.

Then, we can modelate X : ''Number of wafers that pass the test'' as a Binomial random variable.

X ~ Bi(n,p)

Where n = 3 and p = 0.6 is the success probability

The probatility function is given by :

Where is the combinatorial number

Let's calculate f(x) :

For the cumulative distribution function that we are looking for :

The cumulative distribution function for X is :

F(x) = 0           ;  x < 0

         0.064   ;  0 ≤ x < 1

         0.352   ;  1 ≤ x < 2

         0.784   ;  2 ≤ x < 3

            1        ;    x ≥ 3