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.)

Suppose someone wants to sell a piece of land for cash. the selling of a piece of land represents turning econ

Benton company (bc), a calendar year entity, has one owner, who is in the 37% federal income tax bracket (any net capital gains or dividends would be taxed at a 20% rate). bc's gross income is $395,000, and its ordinary trade or business deductions are $245,000. ignore the standard deduction (or itemized deductions) and the deduction for qualified business income. if required, round computations to the nearest dollar. a. bc is operated as a proprietorship, and the owner withdraws $100,000 for personal use. bc's taxable income for the current year is $ , and the tax liability associated with the income from the sole proprietorship is $ . b. bc is operated as a c corporation, pays out $100,000 as salary, and pays no dividends to its shareholder. bc's taxable income for the current year is $ , and bc's tax liability is $ . the shareholder's tax liability is $ . c. bc is operated as a c corporation and pays out no salary or dividends to its shareholder. bc's taxable income for the current year is $ , and bc's tax liability is $ . d. bc is operated as a c corporation, pays out $100,000 as salary, and pays out the remainder of its earnings as dividends. bc's taxable income for the current year is $ , and bc's tax liability is $ .

Acompany using the perpetual inventory system purchased inventory worth $540,000 on account with credit terms of 2/15, n/45. defective inventory of $40,000 was returned 2 days later, and the accounts were appropriately adjusted. if the company paid the invoice 20 days later, the journal entry to record the payment would be