(b) Find the marginal p. d f. of X.

5. (15 points) Let the random vector (X， Y) has a bivariate normal distribution. Show that the best linear predictor of Y with respect to X is given by E[Y|X]. [Note]: For any real-valued functions, g and h，we say that the predictor g(X) is a better estimator of Y than h(X) does，if the m. s. e. of g(X) is less than that of h(X), that is E[Y-g(X)]2 ≤E[Y -h(X)]2.

(a) Find the maximum likelihood estimator of θ .

(b) Does that MLE of θ converges to θ in probability (it is a consistent estimator)? Prove it, if it does.

(1) Inventory turnover.

(2) Profit margin.

(3) Return on total assets.

(15%) 二、 A company’s income statement showed the following: net income, $124,000; depreciation expense, $30,000; and gain on sale of plant assets, $14,000. An examination of the company's current assets and current liabilities showed the following changes as a result of operating activities: accounts receivable decreased $9,400; merchandise inventory increased $18,000; prepaid expenses decreased $6,200; accounts payable increased $3,400. Calculate the net cash provided or used by operating activities.

(10%)三、 Shelby and Mortonson formed a partnership with capital contributions of $300,000 and $400,000, respectively. Their partnership agreement calls for Shelby to receive a $60,000 per year salary. Also, each partner is to receive an interest allowance equal to 10% of a partner’s beginning capital investments. The remaining income or loss is to be divided equally. If the netincome for the current year is $135,000, then what do Shelby and Mortonson，s respective share?

(1) Prepare the general journal entry to record the issuance of the bonds on January 1，2009.

(2) Show how the bonds would be reported on Walker’s balance sheet at January 1，2009.

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