If A and B are mutually exclusive, with P(A) = 0.3, P(B) = 0.5. What is the probability that

•either A or B occurs;

•A occurs but B does not;

•both A and B occur;

•neither A nor B occur;

•A or B but not both?

0.3 The Fibonacci numbers Fn are defined by F1 = 1, F2 = 1 and for n >2, Fn = F sub (n-1) + F sub (n-2). Find a formula for Fn by solving the difference equation.

Find the stationary distribution of this chain

Suppose that the probability it rains today is 0.3 if neither of the last two days was rainy, but 0.6 if at least one of the last two days was rainy. Let the weather on day n, Wn, be R for rain, or S for sun. Wn is not a Markov chain, but the weather for the last two days Xn = (Wn−1 , Wn ) is a Markov chain with four states {RR, RS, SR, SS}.

Suppose MPC is 0.3, use the spending multiplier to fill in the values for an autonomous government spending of $700.

What are some of the problems with the spending multiplier?

(10 Points)

[You must review the literature about the multiplier]

Let A =

| 0.4 −0.3 |

| 0.4 1.2 |

Analyze the long-term behavior of Ak , i.e., lim k→+∞ Ak .

1. In testing the null hypothesis that p = 0.3 against the alternative that p not equal 0.3, the probability of a Type II error is _____________ when p = 0.4 than when p = 0.6.

a. the same

b. smaller

c. larger

d. none of the above

2. During the pre-flight check, Pilot Jones discovers a minor problem - a warning light indicates that the fuel guage may be broken. If Jones decides to check the fuel level by hand, it will delay the flight by 45 minutes. If Jones decides to ignore the warning, the aircraft may run out of fuel before it gets to Gimli. In this situation, what would be:

i) the appropriate null hypothesis? and;
ii) a type I error?

Question 2 options:

) In a market with three assets, the portfolios P₁ = (0.6, 0.3, 0.1) and P₂ = (- 0.2, 0.5, 0.7) lie on the Minimum Variance Set. The portfolios have returns 12% and 4% respectively.

a) Find the portfolio on the MVS with return 14%.

b) Does the portfolio P = (0.1, 0.4, 0.5) lie on the MVS ? Explain.

A 0.3 Kg ball is initially at rest at the top left side of a frictionless incline plane: The incline is 0.25 m height and has a length of 0.65 m.

a) What is the initial Gravitational Potential Energy of the Ball at the top of the incline? b) What will be the final Kinetic energy of the ball at the bottom right side of the incline? c) If there were friction between the ball and the incline, what would happen to the final Kinetic energy of the ball at the bottom of the incline? Increase, decrease, or states the same?

The reaction A + B → C has a ∆G^0’ of -20 kJ/mol at 25 ⁰C. Starting under

       Standard Conditions, one can predict that:

A. at equilibrium, the concentration of B will exceed the concentration of A.

B. at equilibrium, the concentration of C will be less than the concentration of A.

C. at equilibrium, the concentration of C will be much greater than the

     concentration of A or B.

D. C will rapidly break down to A + B.

E. when A and B are mixed, the reaction will proceed rapidly toward formation

     of C.

29. Estimate the value of K_m for an enzyme-catalyzed reaction for which the

      following data points were obtained.

[S] (M)                       V₀ (mM/min)

2.5 x 10^-6                                28

4.0 x 10^-6                                40

1.0 x 10^-5                                70

2.0 x 10^-5                                95

4.0 x 10^-5                                112

1.0 x 10^-4                                128

2.0 x 10^-3                                139

1.0 x 10^-2                                140

A. 1.0 x 10^-4

B. 1.0 x 10^-3

C. 1.0 x 10^-6

D. 1.0 x 10^-5

E. 1.0 x 10^-7

30. pH = pK_a when:

[A^-]/[HA] = 0

log ([A^-]/[HA]) = 1

[A^-] >> [HA]

[A^-] = [HA]

log ([HA]/[A^-]) = 1

31. In the conversion of A into D in the following biochemical pathway, enzymes

       E_A, E_B, and E_C have the K_m values indicated under each enzyme. If all of the

      substrates and products are present at a concentration of 10^-4 M and the

      enzymes have approximately the same V_max which step will be rate limiting?

                                         R_x1      R_x2     R_x3

                                                  A   ↔   B   ↔   C ↔ D

                                                          E_A        E_B       E_C

                                                           K_m =     10^-2M    10^-4M   10^-4M

A. Rx 3         

B. Rx 1         

C. Rx 2         

D. Rx’s 1 and 3

E. Rx’s 2 and 3       

32. Consider the following K_eq values with the appropriate ΔG^0’?

                                       K_eq                                        ΔG^0’

                        A           1.0                           1      28.53

                      B           10^-5                             2     -11.42

                        C           10⁴                          3      5.69

                        D           10²                          4       0

                        E           10^-1                         5      -22.84    

A K_eq of 10² would correspond to which of the following ΔG^0’ values?

28.53

-11.42

5.69

0

-22.84

33. For an enzyme that follows simple Michaelis-Menten kinetics, what is the

      value of V_max if V₀ is equal to 1 µmol minute^-1 when [S] = 1/10 K_m?

11.0 µmol minute^-1

1.10 µmol minute^-1

0.10 µmol minute^-1

10.1 µmol minute^-1

1.0   µmol minute^-1