Victoria is participating in three debates at a speech and debate competition. She has a 60% probability of winning her first debate of the day. Winning a debate increases her probability of winning the next debate by 15%. Losing a debate decreases her probability of winning the next debate by 10%.

1. Are Victoria's results in each debate independent of each other? Explain why or why not.
2. Make a tree diagram to show all possible outcomes of Victoria's three debates. Include the probability of each outcome.
3. Find a probability model for the number of debates Victoria will win in the competition. Describe all important parts of the probability model in the context of Victoria's debate competition, including the random variable, the outcome of the random variable, and the associated probabilities. Use your tree diagram from part (b) to help you.
4. Calculate the number of debates Victoria can expect to win in this competition. Is this a guarantee of the number of debates she will win? Explain.
5. Calculate the variance and standard deviation of the number of debates Victoria can expect to win in this competition. Use the expected value you calculated in part (d).