What was going on when I was born?

Princeton University announced today that it would give 24,000 vertebrate fossils to Yale University. The gift, which includes what is considered one of the world's finest collections of fossils of early mammals, has thousands of items that document the history of mammals after the extinction of the dinosaurs about 60 million years ago, according to paleontologists. Princeton's decision to give the fossils to Yale and largely abandon the field of vertebrate fossil paleontology drew immediate criticism from several paleontologists across the country. But officials of Princeton and Yale hailed the transfer of the collection as a rare example of cooperation in what is usually a highly competitive relationship.

Governor Cuomo announced plans yesterday to put a museum and memorial to Holocaust victims in a new apartment building at Battery Park City. Mr. Cuomo offered the plan as an alternative to housing the museum at the old Federal Custom House, an ornate building that many preservationists said was inappropriate. Under the Governor's proposal, the 34-story Battery Park City building - which had always been part of the planned complex - would be put up by a nonprofit corporation, and what would have been profits would be used to underwrite the museum's operating costs, according to the president of the Battery Park City Authority, Meyer S. Frucher. Spokesmen for the New York City Holocaust Commission said they were excited by Mr. Cuomo's plan and would consider it at a meeting next week. ''We're very pleased,'' said the group's co-chairman, Robert M. Morgenthau, the Manhattan District Attorney.

The Steinbergs are busy cooking matzoh balls for 85 people. The Kaplans are cleaning out their kitchen cabinets and stocking them with ''kosher for Passover'' products. The Kolodneys are studying the Haggadah, the story of the Exodus of the Jews from Egypt in ancient times. The three Teaneck families - belonging to Reform, Orthodox and Conservative congregations, respectively - are preparing for Passover, the weeklong Jewish festival of freedom that begins at sundown Friday with the holiday meal known as the seder.

One of the key suspects in the killing of a United States drug agent was captured early today by the police in Costa Rica, American and Mexican officials said. The suspect, Rafael Caro Quintero, who is believed by authorities to be one of the major figures in Mexico's cocaine and marijuana traffic, was captured in a house that authorities said he owned in San Jose, the Costa Rican capital. Reports from San Jose said he was arrested after United States officials tipped Costa Rican authorities to his presence. Mr. Caro Quintero had been sought by authorities since early February, when an agent of the United States Drug Enforcement Administration, Enrique Camarena Salazar, was abducted on a street in Guadalajara. Mr. Camarena Salazar's beaten body, along with that of a Mexican pilot who sometimes worked with him, was found on a ranch southeast of Guadalajara on March 5.

IN the heart of New York's bustling nightlife, a mime sits perfectly still. Behind him, baby sharks swim in a tank and in front, a clown slumps in a glass display case. These are some of the latest exhibits at Area, the city's most talked-about dance club. The opening of Area more than a year ago gave birth to a new breed of dance club, where music and dance compete with architectural pizazz, where venturesome New Yorkers go almost more to see the latest in props than to listen or move. And now the style is spreading to other clubs in the city.

ONCE a year, and appropriately at the onset of spring, the New York theater sets aside the fretting and the carping, the worrying and the whining, to celebrate youth. The occasion is the Young Playwrights Festival, which opens this weekend at Playwrights Horizons. From the pens of babes - writers from ages 10 to 18, actually - come four one-act plays that will receive full professional productions and five that will receive staged readings. The subjects range from missing children to soldiers at war and the characters include a South Dakota bartender and a punk rocker named Sal Id.

FRIDAY, APRIL 5, 1985 International The President offered a peace plan for Central America. His proposal coupled a call for talks between the Nicaraguan Government and the U.S.-backed rebels with a request to Congress to approve $14 million in aid for the insurgents. Mr. Reagan called for a cease-fire in Nicaragua until June 1. (Page 1, Column 4.) A suspect in the killing of a United States drug agent was captured by the Costa Rican police. The suspect, Rafael Caro Quintero, is believed by authorities to be one of the major figures in Mexico's cocaine and marijuana traffic. (A1:2-3.)

An article and a chart in Business Day on Monday about the stock market's best and worst performers in the first quarter misstated the reason for the 65 percent rise for Williams Electronics Inc. The company's intention to continue seeking acquisitions apparently contributed to the gain. Also, the chart misstated the reason for the decline by the Chicago and North Western Transportation Company. The company lost a bid to acquire the Milwaukee Road.

Three basketball players and five others were indicted today in the Tulane University point-shaving case, and the university's president announced plans to drop Tulane's men's intercollegiate basketball program. The president, Eamon M. Kelly, also said the head coach and two assistants had submitted their resignations. Dr. Kelly said the university had no reason to believe the coaches were involved in any accusations of point- shaving, in which players intentionally hold down their team's score to benefit gamblers. But he said the coach, Ned Fowler, had admitted making illegal payments to players. One report said a star player had told prosecutors that a former assistant coach had paid him $10,000 to attend the university, a charge that the former coach denied, and that Mr. Fowler had paid him $100 a week during the past season. Mr. Fowler refused today to make any substantive comment on the charges.

Robert J. Birnbaum, president and chief operating officer of the American Stock Exchange, was named president and chief operating officer of the New York Stock Exchange yesterday. Mr. Birnbaum's appointment, which had been expected, is apparently the first time a senior official of one exchange has moved to a senior post at the other. Some analysts in the financial community have speculated that the Birnbaum appointment would make a Big Board-American exchange merger more likely, because the New York exchange wants to expand in options trading, an area of strength for the much smaller American exchange.

President Reagan today coupled a call for talks between the Nicaraguan Government and United States-backed rebels with a request to Congress to approve $14 million in aid for the insurgents. In his proposal for peace in Central America, Mr. Reagan called for a cease-fire in Nicaragua until June 1, promising that if Congress agreed to his request for aid for the rebels, the money would not be used for arms before June 1. Nicaragua rejected Mr. Reagan's proposal, calling it a public relations maneuver. (Page A9.)

Japanese Cabinet ministers and political leaders today began to consider a series of measures intended to open Japan's market wider to imports. A senior Foreign Ministry official, however, implied that the proposals might be too vague to end American attacks on Japan's trade policies. ''It won't be concrete,'' the official said of the trade package, which is to be adopted by the Cabinet next Tuesday. But the market-access package - Japan's main effort to head off retaliation threatened by Congress in the past week - probably will be altered in detail before then, and possibly significantly amended, officials said.