what would the effect be of a one-tailed test and the probability of rejecting the null hypothesis?

Two events ?1 and ?2 are defined on the same probability space such that: ?(?1 ) = 0.7 , ?(?2 ) = 0.5 , and ?(?1 ??? ?2 ) = 0.3. a) Find ?(?1 ?? ?2 ). b) Find ?(?1 | ?2 ). c) Are ?1 and ?2 mutually exclusive (disjoint)? and why? d) Are ?1 and ?2 independent? and why?

1. Risk is

a. The probability that return will be less than expected.

b. The standard deviation of the probability distribution of returns.

c. Variability in return

d. All of the above.

2. A stock with a beta of 1.0 will :

a. always generate a return equal to the market average

b. always generate a return that is close to the market average.

c. always generate a return that is at least as the market average.

d. all of the above are correct.

e. none of the above are correct.

3. Syncor borrowed $ 800,000 payable over 5 years, with an interest rate of 9 percent per annum on the unpaid balance. If the loan is to be repaid in 5 equal, end of year payments, what is the total amount of interest paid on this loan?

a. 205656

b. 228278

c. 201753

d. 255131

4. Calculate the required rate of return for Mercury, Inc.. assuming that (1) investors except a 4.0% rate of inflation in the future, (2) the real risk free rate is 3.0% (3) the market risk premium is 5.0%, (4) Mercury has a beta of 1.00 and (5) its realized rate of return has averaged 15.0% over the last 5 years.

a 10.29%

b. 10.83%

c. 11.40%

d. 12%

e. 12.6o%

What is the probability that if a pair of dice is rolled eighteen times, exactly three sums of seven are rolled? (Round your answer to four decimal places.)

Consider the following information on a portfolio of three stocks:

a. If your portfolio is invested 36 percent each in A and B and 28 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., 32.16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16.)

b. If the expected T-bill rate is 4.1 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected risk premium             %

According to a study done by a university​ student, the probability a randomly selected individual will not cover his or her mouth when sneezing is

0.2670.267.

Suppose you sit on a bench in a mall and observe​ people's habits as they sneeze.

​(a) What is the probability that among

1818

randomly observed individuals exactly

55

do not cover their mouth when​ sneezing?

​(b) What is the probability that among

1818

randomly observed individuals fewer than

33

do not cover their mouth when​ sneezing?

​(c) Would you be surprised​ if, after observing

1818

​individuals, fewer than half covered their mouth when​ sneezing? Why?

1). If a couple has two children, what is the probability that they are both girls assuming that the older one is a girl?

2). Suppose that we have two dice, the first one being a regular die, and the second weighted so that half the time it rolls a 1, and half the time it rolls a 2 (it never rolls anything else). If we choose one of these dice at random, and roll a 1, what’s the probability that it is the regular die?

Please give an example of when using the probability an event will occur is important to decision making.  Why?

The rates of return of Stock A and B are distributed as follows:

State Probability Return on A Return on B

1 0.3 15% 5%

2 0.5 9% 7%

3 0.2 -1% 12%

Suppose you have invested $1000 in stock A and $2000 in Stock B. Please, find this portfolio’s expected return and total risk. What is the correlation between the rate of return on Stock A and Stock B?