Vocabulary and short answer

You and your friend are playing a coin toss game where if you toss heads you win $1, and if you toss tails you lose $1. You toss nine heads in a row and your friend is getting frustrated because they're running out of money. They think they are "due" to win the next toss because it would break the streak. Is this true? Explain to your friend why or why not this is the case.

Read the following scenario and explain why the doctors conducting the research could establish causality without doing an experiment. Doctors had long observed that most cancer patients were smokers. A series of observational studies comparing smokers and "similar" nonsmokers showed a strong association with smoking and death from lung cancer. The subjects were similar in the sense of characteristics such as age, gender, and overall health.

In a game of chance, you find the expected value of a single outcome is a loss of $0.43. What would the expected outcome of 1 round of this game? What about 1,000 rounds?

You are considering purchasing a small herd of goats. In order to ensure your new herd of goats against things such as alien abduction, sink holes, corona virus, train derailments, and accidental dynamite explosions, you will have to pay the insurance company $800 per year. Upon further research, you find that the expected value of each policy is $255.

a. What is the value of the policy to you? b. What is the value of the policy to the insurance company? c. Explain why this is a good bet for the insurance company?

What is the difference between a point estimate and an interval estimate? Explain which one of the two is more accurate and why that is the case.