01-10-2018

Problem 1. Consider the experiment of rolling a fair dice.  Let the random variable X denote the number that turns up.

• 1. What are the values this random variable can take?

  2. Is it a discrete or a continuous random variable?

  3. What is the probability distribution function? Is it uniform?

  4. What is its expected value? Interpret this result.

Problem 2. Consider the experiment of tossing a fair coin 3 times. Let the random variable X denote the number of heads that occur in the three tosses.

• 1. What are the values this random variable can take?

  2. Is it a discrete or a continuous random variable?

  3. What is its probability distribution function?

  4. What is the expected value of X? Can this value really occur? Interpret this result.

  5. Suppose I tell you that for every heads that turns up in the three coin tosses, I’ll pay you 2$, but if three tails show up you must pay me 20$. Will you play this game with me? Is it fair?

  6. What should be the amount I receive for 3 tails, for the game in part e to be fair?