BORN. To Caroline, 27, Princess of Monaco, and her husband of 5 1/2 months, Stefano Casiraghi, 23, Italian businessman: a son, their first child and heir to the principality after his uncle Prince Albert; in Monte Carlo. Name: Andrea-Albert Grace. Weight: 6 Ibs. 6 oz.

ENGAGED. Kathleen Turner, 29, sleek and sexy movie actress (Body Heat, Romancing the Stone); and Jay Weiss, 29, New York City real estate developer. The wedding, the first for both, is set for August.

ENGAGED. Sigourney Weaver, 34, cool, willowy actress (The Year of Living Dangerously, Ghostbusters); and Jim Simpson, 28, a theatrical director; in Honolulu. The marriage will be the first for both.

DIED. Fuad Mohieddin, 58, Prime Minister of Egypt since January 1982, secretary-general of the ruling National Democratic Party, and No. 2 man in the regime of President Hosni Mubarak; of a heart attack, following a seizure three weeks ago that was aggravated by his refusal to follow doctors' orders to abandon strict fasting during the holy month of Ramadan; in Cairo. A Deputy Prime Minister under President Anwar Sadat, Mohieddin formed the first Mubarak Cabinet after Sadat's assassination in October 1981. Though Mubarak praised him as having done his duty "to perfection," the Prime Minister had been criticized for his purported reluctance to carry out democratic reforms the President had advocated.

DIED. J. Paul Lyet, 67, chairman from 1972 to 1982 of Sperry Corp.; of cancer; in New York City. A C.P. A. from a brass-knuckled North Philadelphia slum, he was working for the New Holland farm machinery company when it was taken over by Sperry in 1947; he kept that operation running profitably during the 1960s when the company's Univac division was bungling its head-to-head computer competition with IBM. As Sperry's boss, he more than tripled revenues to $5.6 billion, pushed for high-tech sales to the Soviet Union, expanded ex ports so that 44% of Sperry's business was overseas, then saw foreign currency and interest fluctuations curtail company earnings before his retirement.

DIED. Peter C. Wilson, 71, English art salesman extraordinary and longtime chairman of Sotheby's, the world's leading art-auction firm, who was responsible for transforming the genteel, Old World establishment into a glamorous high-tech $575 million-a-year business; of the effects of diabetes; in Paris. After joining Sotheby's in 1936 as a porter, the normally reticent Wilson became a nonpareil auctioneer, dubbed the "fastest gavel in the West." Rising to chairman in 1958, he set about overseas expansion, establishing offices in Europe, Asia, Latin America and the U.S., notably in New York City with the acquisition of Parke Bernet. His taste, timing and towering presence (6 ft. 4 in.) helped him to engineer precedent-breaking sales, including the first auction (1965) to use a television satellite to connect London and New York showrooms.