At the one top pizza shop, mushrooms are the only topping. curiously, a pizza sold before noon has mushrooms with probability p = 1/3 while a pizza sold after noon never has mushrooms. also, a pizza is equally likely to be sold before noon as after noon. on a day in which 100 pizzas are sold. let n equal the number of pizzas sold before noon and let m equal the number of mushroom pizzas sold during the day.

a)what is the conditional pmf of m given n? are m and n independent?

b)what is the joint pmf of m and a/?

Last year, western corporation had sales of $5 million, cost of goods sold of $3 million, operating expenses of $175,000 and depreciation of $125,000. the firm received $40,000 in dividend income and paid $200,000 in interest on loans. also, western sold stock during the year, receiving a $40,000 gain on stock owned 6 years, but losing $60,000 on stock owned 4 years. what is the firm's tax liability?

The 39 percent and 38 percent tax rates both represent what is called a tax "bubble." suppose the government wanted to lower the upper threshold of the 39 percent marginal tax bracket from $335,000 to $208,000. what would the new 39 percent bubble rate have to be? (do not round intermediate calculations. enter your answer as a percent rounded to 2 decimal places,e.g., 32.16.)

Google started as one of many internet search engines, amazon started as an online book seller, and ebay began as a site where people could sell used personal items in auctions. these firms have grown to be so large and dominant that they are facing antitrust scrutiny from competition regulators in the us and elsewhere. did these online giants grow by fairly beating competition, or did they use unfair advantages? are there any clouds on the horizon for these firms -- could they face diseconomies of scale or diseconomies of scope as they continue to grow? if so, what factors may limit their continued growth?