hw100a_6_f10 - University of California Los Angeles...

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University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Homework 6 EXERCISE 1 A coin is tossed 3 times independently. One of the variables of interest is the number of tails X . Let Y denote the amount of money won on a side bet in the following manner: If the first tail occurs on the first toss, you win $1. If the first tail occurs on the second toss, you win $2. If the first tail occurs on the third toss, you win $3. If no tails appear you lose $1. Construct the joint probability distribution of X and Y . In other words complete the following table where the entries are the probabilities for each pair of values of the variables X and Y . X Y 0 1 2 3 -1 ? ? ? ? 1 ? ? ? ? 2 ? ? ? ? 3 ? ? ? ? EXERCISE 2 A die is rolled and the number observed X is recorded. Then a coin is tossed number of times equal to the value of X . For example if X = 2 then the coin is tossed twice, etc. Let Y be the number of heads observed. Note: Assume that the die and the coin are fair.
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