You are a contestant on a television game show. Before you are three closed

doors. One of them hides a car, which you want to win; the other two hide

goats (which you do not want to win).

First you pick a door. The door you pick does not get opened immediately.

Instead, the host opens one of the other doors to reveal a goat. He will then

give you a chance to change your mind: you can switch and pick the other

closed door instead, or stay with your original choice. To make things more

concrete without losing generality concentrate on the following situation

(a) You have chosen the first door.

(b) The host opens the third door, showing a goat.

If you dont switch doors, what is the probability of wining the car? If you

switch doors, what is the probability of wining the car? Should you switch

doors?

14. Linda is 31 years old, single, outspoken and very bright. She majored in

philosophy. As a student she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations. Which is more probable?

(a) Linda is a bank teller?

(b) Linda is a bank teller who is active in the feminist movement?

1. A teacher wishes to know whether the males in his/her class have more

conservative attitudes than the females. A questionnaire is distributed assessing

attitudes and the males and the females are compared. Is this an example of

descriptive or inferential statistics?

2. A cognitive psychologist is interested in comparing two ways of presenting

stimuli on sub- sequent memory. Twelve subjects are presented with each method

and a memory test is given. What would be the roles of descriptive and

inferential statistics in the analysis of these data?

3. If you are told only that you scored in the 80th percentile, do you know from

that description exactly how it was calculated? Explain.

4. A study is conducted to determine whether people learn better with spaced or

massed practice. Subjects volunteer from an introductory psychology class. At

the beginning of the semester 12 subjects volunteer and are assigned to the

massed-practice condition. At the end of the semester 12 subjects volunteer and

are assigned to the spaced-practice condition. This experiment involves two

kinds of non-random sampling: (1) Subjects are not randomly sampled from

some specified population and (2) subjects are not randomly assigned to

conditions. Which of the problems relates to the generality of the results? Which

of the problems relates to the validity of the results? Which problem is more

serious?

5. Give an example of an independent and a dependent variable.

6. Categorize the following variables as being qualitative or quantitative:

Rating of the quality of a movie on a 7-point scale

Age

Country you were born in

Favorite Color

Time to respond to a question

2. Let X1, X2, ..., Xn be independent continuous random sample from the distribution that has cumulative distribution function F(x) and probability density function f(x). Find the joint probability density function and joint cumulative distribution function of X(1) and X(n), where X() is the smallest ordered statistic and X(m) is the largest ordered statistic among X1, X2. ... . Xn. (20 points)31 Joint Cumulative Distribution Function Sketch the joint cumulative distribution function (CDF) for the joint probability mass func- tion (pmf) represented in Figure 8. For each region of the CDF with a constant value, indicate on the xy plane the value of the CDF and its corresponding boundaries. y PxY [X = x, Y = y] -1 Figure 8. Joint probability mass function (pmf) P[X = x, Y = y].5. (35 points) Suppose that two random variables X and Y have a joint probability density function f(x, v) = / be (2:+3)/6 for z > 0 and y > 0, otherwise. (a) Are the two random variables X and Y independent? Explain. (b) Find the joint cumulative distribution function (cdf), Fx.y(u, v). (c) Find P(0 2 X = 1).5. Let X and Y be random variables with the following joint probability density function (PDF): f(x, y) = or'(Ity) 15