Question

An optical inspection system is used to distinguish among different part types. The probability of a correct classification of any part is 0.93. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts that are correctly classified. Determine the probability mass function of X.

Probability Mass Function of X
x f(x)
0
1
2
3

Answer 1

Follows are the solution to this question:

Explanation:

Let P(X = x) mark x model number classified correctly.

The mass function of the probability:

`\to f(0) = P(X=0) = (0.03)^3 = 0.0000\\\\\to f(1) = P(X=1) = (3 C_1)* (0.97)* (0.03)^2 = 0.0026\\\\\to f(2) = P(X=2) = (3 C_2)* (0.97)^2 * (0.03) = 0.0847\\\\\to f(3) = P(X=3) = (0.97)^3 = 0.9127\\\\`

`x \ \ \ \ f(x) \\\\0\ \ \ \ 0.0000\\\\1\ \ \ \ 0.0026\\\\2\ \ \ \ 0.0847\\\\3\ \ \ \ 0.9127`