Question 6 part 1

> Assignment 2 Questions (PDF, for previewing only) t 2 Questions (PDF, for previewing only) ~ c. 9% of all components are detective! (Hint - treat this as a discrete random variable with two outcomes with probabilities outlined above, and compare the "expected" or "mean" cost using the formula that you wrote in part i. of this question with the certain cost of pre-testing components before installing). 6. Consider the binomial distribution with n - 5 and 7 = 0.2 hence the random variable X E {0, 1, . .., 5} (this question is worth 4 marks). i. Calculate the mean and variance of this random variable using the E(X) - >, Tip(X = Ti) type formulas for each (i.e., the formulas for computing the mean and variance of any discrete random variable). ii. Repeat i. above using the short-cut formula (i.e., compute the mean and variance using the formulas depending only on 7 and n that are specific to the binomial distribution). 7. Suppose that the subjective prior probabilities of finding oil are p(oil)-0.5 and p( no oil)=0.5. Your company drills for 500ft and finds no oil, but they sample the soil at 500ft. From experience the company knows that the conditional probability of finding this type of soil given that oil is present is 0.1, while the probability of finding this type of soil given that no oil is present is 0.9. What is the posterior probability of finding oil (i.e., the probability of finding oil given that this type of soil is present)? You must show all of your work (hint - think "Reverend Thomas Bayes", and you can use the symbols S and S for "this type of soil" and "not this type of soil", respectively, the symbols O and O for "oil" and e here to search 9 R PDF 55%