6. Let X1, X2, X3 be a random sample from the uniform distribution on the

interval (0, 1). What is the probability that the sample median is less than

0.4?

7. Let X1, X2, X3, X4, X5 be a random sample from the uniform distribution

on the interval (0, ?), where ? is unknown, and let Xmax denote the largest

observation. For what value of the constant k, the expected value of the

random variable kXmax is equal to ??

8. A random sample of size 16 is to be taken from a normal population having

mean 100 and variance 4. What is the 90th percentile of the distribution of

the sample mean?

A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow

marble. Two marbles are chosen (without replacement). (a) What is the

probability that one will be green and the other red? (b) What is the probability

that one will be blue and the other yellow?

10. You roll a fair die five times, and you get a 6 each time. What is the probability

that you get a 6 on the next roll?

11. You win a game if you roll a die and get a 2 or a 5. You play this game 60

times.

a. What is the probability that you win between 5 and 10 times (inclusive)?

b. What is the probability that you will win the game at least 15 times?

c. What is the probability that you will win the game at least 40 times?

d. What is the most likely number of wins.

e. What is the probability of obtaining the number of wins in d?

Explain how you got each answer or show your work.

12. In a baseball game, Tommy gets a hit 30% of the time when facing this pitcher.

Joey gets a hit 25% of the time. They are both coming up to bat this inning.

a. What is the probability that Joey or Tommy will get a hit?

b. What is the probability that neither player gets a hit?

c. What is the probability that they both get a hit?

13. An unfair coin has a probability of coming up heads of 0.65. The coin is flipped

50 times. What is the probability it will come up heads 25 or fewer times?

(Give answer to at least 3 decimal places).

14.You draw two cards from a deck, what is the probability that:

a. both of them are face cards (king, queen, or jack)?

b. you draw two cards from a deck and both of them are hearts?

5. Let X and Y be random variables with the following joint probability density function (PDF): f(x, y) = or'(Ity) 15