Let X ∼ Exp(λ) with pdf f(x|λ) = λe−λx and λ ∼ Gamma(a, b) with PDF f(λ) = 1 λa−1e−λ/b where a > 0 is the shape parameter and b > 0 is the scale parameter. That Γ(a)ba is to say, the Poisson parameter λ is no longer a constant number; it is a gamma random variable. Find the marginal distribution of X, i. e., write the PDF of X as a function of a and b. (Note that this marginal distribution is called Lomax distribution.)

Pettijohn inc. the balance sheet and income statement shown below are for pettijohn inc. note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during the next 5 years, and the notes payable will be rolled over. balance sheet (millions of $) assets 2016 cash and securities $ 1,554.0 accounts receivable 9,660.0 inventories 13,440.0 total current assets $24,654.0 net plant and equipment 17,346.0 total assets $42,000.0 liabilities and equity accounts payable $ 7,980.0 notes payable 5,880.0 accruals 4,620.0 total current liabilities $18,480.0 long-term bonds 10,920.0 total debt $29,400.0 common stock 3,360.0 retained earnings 9,240.0 total common equity $12,600.0 total liabilities and equity $42,000.0 income statement (millions of $) 2016 net sales $58,800.0 operating costs except depr'n $54,978.0 depreciation $ 1,029.0 earnings bef int and taxes (ebit) $ 2,793.0 less interest 1,050.0 earnings before taxes (ebt) $ 1,743.0 taxes $ 610.1 net income $ 1,133.0 other data: shares outstanding (millions) 175.00 common dividends $ 509.83 int rate on notes payable 1. what is the firm's current ratio? (points : 6) 0.97 1.08 1.20 1.33 2. what is the firm's quick ratio? (points : 6) 0.49 0.61 0.73 0.87 3. what is the firm's total assets turnover? (points : 6) 0.90 1.12 1.40 1.68 4. what is the firm's inventory turnover ratio? (points : 6) 4.38 4.59 4.82 5.06 5. what is the firm's debt ratio? (points : 6) 45.93% 51.03% 56.70% 70.00% 6. what is the firm's roa? (points : 6) 2.70% 2.97% 3.26% 3.59% 7. what is the firm's roe? (points : 6) 8.54% 8.99% 9.44% 9.91%

The green fiddle has declared a $5 per share dividend. suppose capital gains are not taxed, but dividends are taxed at 15 percent. new irs regulations require that taxes be withheld at the time the dividend is paid. green fiddle stock sells for $71.50 per share, and the stock is about to go ex-dividend. what will the ex-dividend price be?

If a product goes up in price, and the demand for it drops, that product's demand is a. elastic b. inelastic c. stable d. fixed select the best answer from the choices provided