3. (7%) (8%) Let X = Rcosθ and Y a Rsin θ, where R is a positive random variable on
(0,∞), θ is a uniform random variable on (0, 2π), and R and θ are mutually independent.
Derive the corresponding distributions of X/Y and 2XY/
二、閱讀測驗:下面三篇短文共有 15 題,每篇各有 5 題,為第 16 – 30 題,請閱讀短文後,選出最適當的答案。 ▲ 閱讀下文,回答第 16 − 20 題 Meet the People’s Company. Like a democracy, it can be a noisy place where citizens sometimes think the people in charge have no idea what they’re doing. But at eBay, the online auction site, the people are in charge. Its customers – the 70 million buyers and sellers who trade here – have the kind of influence that most consumers and businesses can only dream of. It’s true, eBay has a business model that doesn’t require carrying any inventory. But the real secret of eBay’s unlikely success is this: it’s a master at capturing the awesome communication power of the Internet and tracking customers’ every movement, so new products and services are tailored to just what they want. ( ① ) eBay’s customers are its product development, market research, merchandising, and sales department – all rolled into one. It’s not just that they have made eBay into a global marketplace for almost anything, from a $1 baseball card to a $4.9m Gulfstream jet, eBay’s customers also tell the world about eBay by word of mouth. ( ② ) They crowd online discussion boards, share tips, point out problems, and lobby for changes. eBay’s customers even police the site by rating each other. Imagine a retailer trying to do this: interview every single person leaving every store, post a list of what each thought of the shopping experience, ask them to write up a merchandising plan and call suppliers to arrange deliveries – and oh, by the way, could they keep an eye out for shoplifting? That’s what eBay’s customers voluntarily do each day. Back in 1995, when Pierre Omidyar unveiled Auction Web, he had much more in mind than simply helping his girlfriend trade Pez dispensers. He aimed to create a market for a wide range of goods, but with a difference. “I wanted to give the power of the market back to individuals,” says Omidyar. But his biggest breakthrough was the Feedback Forum, a rating system that made it easy for buyers and sellers to grade each transaction. Amazingly, it worked. And positive ratings, which translated to more sales, kept people from going to other sites. ( ③ ) Since early 1999, eBay has regularly flown sellers and buyers to its headquarters in California to interview them, asking for their views on new features and policies. The result: fewer problems. Even when something does go wrong, eBay can respond quickly. eBay business is the company’s latest offering, a new site providing businesses with an e-commerce platform. ( ④ ) However, many rivals aim to be the biggest places for e-commerce as well, and some are making fast progress. But there’s a bigger question: can eBay’s values survive such grand ambitions? Omidyar worries that the growing participation of large commercial sellers could dilute eBay’s unique culture. eBay’s people power makes building a business simple compared with everything conventional companies must do. Keeping in touch with all those customers from here on won’t be easy.
【題組】19. What is the main secret to eBay’s success?
(A) cutting the inventory cost
(B) cooperating with its major rivals
(C) hiring its customers to safeguard its site
(D) giving the power of the market back to individuals