1.)  State the conditions for this to be a valid probability model:

5.)  Find the expected value of the random variable:

6.)  Given that the variance of this distribution is 90, determine the mean and standard deviation of the random variable Y where Y = 3 + 2X

7.)  Suppose you draw two numbers at random from this distribution.  What is the mean and standard deviation of the sum of these two numbers?

8.)  Find P(X = 6)?

9.)  Find P(X < 5)?

10.)  What is the median of X?

11.)  Fill in  a venn diagram representing this situation.

12.)  Suppose an individual is drawn at random from this population.  Find the following probabilities.

13.)  Are these two events mutually exclusive?  Explain.

14.)  Are these two events independent?  Explain.

15.)  Complete the following tree diagram representing this situation.

16.)  If a computer is brought in by a customer, what is the probability that Bob will be able to fix it?

17.)  If Bob was able to fix a computer, what is the probability that it was infected by virus Dummy?

18.)  What is the probability that your first win will occur on your third play of the game?

19.)  What is the probability that your first win will occur before your 5 play of the game?

20.)  How many times do you expect to have to play before winning the first time?

21.)  If you play the game 20 times, how many times to you expect to win?

22.)  What is the probability that you win exactly 6 times out of 20 games played?

23.)  What is the probability that you win at least 4 times out of 20 games played?

24.)  What is the standard deviation of the number of games you will win out of 20 games played?