(a) Find the value of c

(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.

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