For the remaining questions: Let W be a random variable representing the results of a coin ip (l = heads, 0 = tails). You observe a random sample of 100 coin tosses. 70 out of the 100 tosses yielded heads. You are suspicious that the coin is not fair (i.e., equal probability of heads and tails) and want an estimator for the E (W) = my. Let Var(W) = 0%,. 2. Is your random sample lid? Explain. 3. Calculate the sample average, W: You are debating between using three different estimators for MM: 1. W: Sample Average 2. W1: the resuit of the first toss 3. W5 = W1 + W2: the summation of the first two tosses 4. Calculate the bias of each of these estimators: 5. Based on unbiasedness, which of the estimators do you eliminate? Of the remaining two estimators, 6. Are both estimators consistent? Prove your answer. 7. Based on efciency, which estimator do you choose to use? You're ready to test if the coin is fair. 8. State your null and alternative hypothesis: 9. Calculate your test statistic: 10. What do you conclude (be careful in wordingg 11. What is your 95% condence interval for aw? 12. Draw a picture describing your hypothesis testing