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 following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets.

(a) Use regression to find a quadratic model for the data. (Round the regression parameters to two decimal places.)
R =

(b) Calculate

R(65).

(Round your answer to two decimal places.)

R(65) =

Explain what your answer means in practical terms.

Commercial vehicles driving at night on urban streets at  miles per hour have traffic accidents at a rate of  per 100,000,000 vehicle miles.

(c) At what speed is vehicular involvement in traffic accidents (for commercial vehicles driving at night on urban streets) at a minimum? (Round your answer to the nearest whole number.)
mph