Problems

1. (10 points) Textbook problem 9.2
2. (10 points) Textbook problem 9.3
3. (10 points) Textbook problem 9.4
4. (10 points) Textbook problem 9.9
5. (10 points) For each of the following situations, write down the likelihood function \( L(\theta) \), where \( \theta \) is the probability of heads for the coin described.
   1. You toss a coin 50 times and see that it came up heads 35 times and tails 15 times.
   2. You toss a coin 100 times and see that it came up heads 54 times and tails 45 times. You don't know which way it came up the last time because it rolled into a drain was lost.
   3. You decide to toss a coin until it comes up heads the first time and then toss it 10 more times. It first comes up heads on the third toss and then comes up heads 5 more times in 10 tosses.
6. (Extra 3 points) Textbook problem 9.13