Question

An assembly consists of three mechanical components. Suppose that the probabilities the first, second, and third components meet specifications are 0.95, 0.98, and 0.99 respectively. Assume that the components are independent. Determine the probability mass function of the number of components in the assembly that meet specifications.

Answer 1

The probability mass function (PMF) of the number of components in the assembly that meet specifications can be determined using the multiplication rule. The PMF gives the probabilities for each possible value of the random variable. The PMF can be represented as a table or a graph.

Step-by-step explanation:

The probability mass function (PMF) gives the probabilities of all possible values of a random variable. In this case, the random variable is the number of components in the assembly that meet specifications.

Since the components are independent, we can use the multiplication rule to find the probability that a specific number of components meet specifications. The PMF can be calculated as follows:

P(X = 0) = (1 - 0.95) * (1 - 0.98) * (1 - 0.99)

P(X = 1) = 0.95 * (1 - 0.98) * (1 - 0.99)

P(X = 2) = 0.95 * 0.98 * (1 - 0.99)

P(X = 3) = 0.95 * 0.98 * 0.99

The PMF can be represented as a table or as a graph, with the x-axis representing the number of components meeting specifications and the y-axis representing the corresponding probabilities.