Problem 1.1

Not all probability distributions or their inverse are always easy to calculate, e.g. using Excel functions. In such cases, simulation can often be used. Here are a couple of such problems for you to simulate. For each example, simulate 500-1000 replications of the experiment.

1. You observe a sequence of parts from a manufacturing line. These parts use a component that is supplied by one of two suppliers. Each part made with a component from supplier 1 works properly with a probability of 0.95, and each part made with a component from supplier 2 works properly with a probability of 0.98. Assuming that 100 of these parts are made, 60 from supplier 1 and 40 from supplier 2, you want to find the probability that at least 97 of them work properly.
2. Here we look at a more generic example such as coin-flipping. There is a sequence of trials where each trial is a success with probability p and a failure with probability 1 p. A run is a sequence of consecutive successes or failures. For most of us, intuition says that there should not be long runs. Test this by finding the probability that there is at least one run of length at least six in a sequence of 15 trials. (The run could be of 0s or 1s.) You can use any value of p you likeor try different values of p.