State whether each of the following variables

are examples of an independent variable or

quasi-independent variable. Only answer quasiindependent for variables that can't be randomized.

a. Marital status

b. Political affiliation

c. Time of delay prior to recall

d. Environment of research setting

e. Years of education

f. Type of feedback (negative, positive)

19. To determine whether a new sleeping pill was

effective, adult insomniacs received a pill (either

real or fake), and their sleeping times were subsequently measured (in minutes) during an overnight observation period.

a. Identify the independent variable in this study.

b. Identify the dependent variable in this study.

20. A researcher tests whether cocaine use increases

impulsive behavior in a sample of cocaine-dependent and cocaine-inexperienced mice.

a. Identify the independent variable in this study.

b. Identify the dependent variable in this study.

21. Researchers are interested in studying whether

personality is related to the month in which

someone was born.

a. What scale of measurement is the month of

birth?

b. Is it appropriate to code the data? Explain

How many chords can be drawn through 21 points on a circle?

4. How many triangles can be formed by joining the vertices of a hexagon?

5. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels

can be formed?

6. If four dice are rolled, find the number of possible outcomes in which atleast one

die shows 2.

7. There are 18 guests at a dinner party. They have to sit 9 guests on either side of

a long table, three particular persons decide to sit on one particular side and two

others on the other side. In how many ways can the guests to be seated?

8. If a polygon has 44 diagonals, find the number of its sides.

9. In how many ways can a cricket team of 11 players be chosen out of a batch of 15

players?

(i) There is no restriction on the selection.

(ii) A particular player is always chosen.

(iii) A particular player is never chosen.

10. A Committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways this

can be done when

(i) atleast two ladies are included

(ii) atmost two ladies are include

(4) Is the Markov chain whose transition matrix whose transition matrix is 0 0.4 0.67 regular? (Yes or No) (5) Is the Markov chain whose transition matrix whose transition matrix is 0.2 0 0.8 0.6 0.4 0 regular? (Yes or No)[3+4+4+2=13 points] Problem 3. Consider a Markov chain with three states {51, 53, 53}, and the following transition matrix: If? 1,!2 1'} A: a 1:3 233 2,33 a 1,?3 1} Draw the state diagram, annotated with transition probabilities for Markov chain. 2} l[liven that the initial distribution on = {1,,}, what is the probability,' that the chain is in state .32 after 2 steps. 3} Find the stead}.r state distribution for this Markov chain. 4} Suppose that for a single visit to state 5, you receive f[s] dollars, where sl) = 1,1152} 2 2, and f[53} = 3. When the Markov chain reaches steady state, what's the value of E[ f [1(2)]? Exercise 9.2.4 Consider a discrete-time Markov chain consisting of four states a, b, c, and d and whose transition probability matrix is given by 0.0 0.0 1.0 0.0 0.0 0.4 0.6 0.0 P = 0.8 0.0 0.2 0.0 0.2 0.3 0.0 0.5 Compute the following probabilities: (a) Prob( X4 = c, X3 = c, X2 = c, X1 = c | Xo = a). (b) Prob(X6 = d, Xs = C, X4 = b | X3 = a). (c) Prob(Xs = c, X6 = a, X, = c, X8 = c | X4 = b, X3 = d)