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: A manufacturer of an integrated circuit tests a sequence of circuits until it sees a failure

Also, enumerate the outcomes associated with following event: The set B corresponding to the event “it takes more than 4 test before seeing the first failure”.

Answer 1

A manufacturer of an integrated circuit tests a sequence of circuits until it sees a failure.

So there are two possible outcomes as "The result of the integrated circuit tests is failure" and "The result of the integrated circuit tests is not failure"

Let X be a random variable which takes the number of test to see the first failure.

So that the possible values of X are 1,2,3,....

So sample space of a random variable X is  Ω = { 1, 2, 3, ....}

Let B = “it takes more than 4 test before seeing the first failure”

So the possible values of X corresponding to B are 5, 6, 7, and so on.

Therefore B = { 5, 6, 7, ....}