Frank, a rational investor, has $2,000 to invest for one year while she completes her professional accounting designation. She is contemplating investing the full amount in shares of Northern Oil & Gas Ltd. (a1) or in a risk-free government bond yielding an annual return of 3.2% (a2). Frank identifies two states of nature:

State H: Northern has high future cash flow.

State L: Northern has low future cash flow.

On the basis of her prior information about Northern, Frank assesses the following subjective prior state probabilities:

State H: 0.4

State L: 0.6

The following is the payoff table for these two investments. Payoffs from Northern shares include dividends and estimated capital gain for the year. Capital gain is based on the average analyst forecast for Northern's share price. Payoffs are net of (i.e., they exclude) the original investment.

STATE

H L

ACT A1 484 25

ACT A2 64 64

The investor is risk adverse, with utility equal to the square root of the net dollar payoff.

a. On the basis of her prior probabilities, which act should Frank take? Show calculations.

b. Instead of acting now, Frank decides to obtain more about Northern by reading its annual report. He knows that financial statements are based on a mixed measurement model. Also, he is a student of financial accounting theory, and estimates the quality of financial statements prepared according to these standards by the following information system:

GOOD BAD

H 0.7 0.3

L 0.1 0.9

Good evidence means that a company reports profits that are higher than the average analyst forecast. Bad evidence means that the company's profits are less than forecast.

Upon reading the current annual report, Frank finds it is good. Which act should Frank take now? Show calculations.

C. After buying Northern shares, Frank is disappointed to note that the market price of its shares begins to fall, despite the good news in its earnings report. She now suspects that the good news in Northern's financial statements was not as good as she originally believed. Is this possible? Give reasons why or why not.

A subset of individuals from whom data are collected Sample [ Choose Univariate statistics Numbers and graphs used to provide Continuous variables basic information about a sample Descriptive statistics Bivariate statistics Population An entire group of individuals from Cumulative percentages whom we are usually unable to collect Dispersion Central tendency data but to whom we want to make Sample inference Inference Methods used to describe a single Univariate statistics variable Statistics describing the middle of a Central tendency distribution The process of using a sample to Inference describe a population Statistics describing the spread of a Dispersion distribution Methods used to describe the Bivarlate statistics relationship between two variablesBased on the graph depicting the relationship between two variables, you would conclude the 10 .. ... variable 2 4 ... ... N O a b C variable 1 ()A. independent variable: discreteominal; relationship best tested with univariate test (e.g. analysis of variance) ). independent variable: continuous; relationship best tested with bivariate test (e.g. linear regression) " dependent variable: discreteominal; relationship best tested with contingency test (e.g. chi-square) dependent variable: continuous; relationship best tested with bivariate test (e.g. linear regression)AP 2: Take a look at Example 5d on page 253 - the bivariate normal distribution. Suppose that (X, Y) are bivariate normal random variables with means ux, by, variances Ox, oy >0, and correlation pe (-1, 1). They have joint density -1 2 2 f(I, y) = I- HX y - HY (x - ux) (y - HY) 2noxoy v1 - p2 exp + 2(1 - p2) - 2p OX y OXOY Show that the conditional distribution of X given {Y = y} is (univariate) normal. What is X's conditional mean and conditional variance