Question

Circuit boards from two assembly lines set up to produce identical boards are mixed in one storage tray. As inspectors examine the boards, they find that it is difficult to determine whether a board comes from line A or line B. A probabilistic assessment of this question is often helpful. Suppose that the storage tray contains 10 circuit boards of which six came from line A and four from line B. An inspector selects two of these identical-looking boards for inspection. He is interested in X, the number of inspected boards from line A.

a. Find the probability function for X .
b. Graph the probability function of X .
c. Find the distribution function of X .
d. Graph the distribution function of X .

Answer 1

a) X = 2/15 , 8/15, 1/3

b) attached below ( probability plot )

C) F(x ) attached below

d) cumulative probability plot

Explanation:

a) Determine the probability of Function X

P( x = 0 ) = 6 / 45 = 2 /15 = 0.1333

P( x = 1 ) = 8/15 = 0.5333

P( x = 2 ) = 1/3 = 0.3333

Hence the probability of Function X = 2/15 , 8/15, 1/3

b) Graph of the probability Function of X

x 0 1 2

p(x) 0.1333 0.5333 0.3333

attached below is the plot ( probability plot )

c) Determine the Distribution function of CX

using the results achieved in part ( a )

attached below is the solution

d) Graph of distribution function of X

x 0 1 2

p(x) 0.1333 0.6667 1

attached below is the plot ( cumulative probability plot )