Question

Q. 1 For each of the following experiments explicitly write down, enumerate or describe the sample space Ω, the possible outcomes of the experiment and possible events associated with the experiment:

1. A manufacturer of an integrated circuit tests 4 circuits in a row to determine whether each meets quality objectives

Answer 1

A manufacturer of an integrated circuit tests 4 circuits in a row.

So that the number of trials = 4

Each trial either meet quality objectives ( called as success) or not meet the quality objectives(called as failure).

That is there are only two outcomes as success and failure.

Let's defined the random variable X as "the number of circuits who meet the quality objectives"

Therefore X takes the values as 0, 1, 2, 3, 4.

So that the sample space Ω = {0, 1, 2, 3, 4 }.

Also the test of each circuits are independent to each other.

Therefore X follows binomial distribution with parameter n = 4 and p = probability of a circuits who meet the quality objectives.