Discuss the below:
Q1. A production line produces good articles with probability .7, average ones with probability of .2, and defective ones with probability .1. Ten articles are selected.
a) What is the probability of 8 good ones and 1 defective?
b) What is the probability that there is an equal number of good and defective articles?
Q2. A person decides to throw a pair of dice until he gets 2 sixes. What is the expected number of throws until he stops?
Q3. A transistor manufacturer claims its product has 10% defectives. A sample of 15 transistors is examined and 3 are found to be defective. Would you reject their claim with alpha <= 0.05?
Q4. An experiment is set to test the hypothesis that a given coin is unbiased. The decision rule is the following: Accept the hypothesis if the number of heads in a sample of 200 tosses is between 90 and 110 inclusive, otherwise reject the hypothesis.
a) Find the probability of accepting the hypothesis when it is correct.
b) Find the probability of rejecting the hypothesis when it is actually correct.