Marlene Hess and her bandaged daughter BranDee sat in the Red Dog Cafe this morning trying to figure out why it happened here.

BranDee, a fifth-grader at Cokeville Elementary School, was burned on her fingers, forearm and chest when a gasoline bomb detonated in a classroom Friday afternoon.

David and Doris Young had herded 150 children into the room. The couple carried rifles and explosives, including milk bottles filled with gasoline, and demanded a $300 million ransom. David Young, a former Cokeville town marshal, told his wife to hold the bomb's detonator while he went to the restroom. After it exploded, David Young ran back and fatally shot himself in the head.

"I'm glad they're dead. They put a gun to my teacher's head," said BranDee, one of 79 people burned in the explosion. Two adults and 11 students remain hospitalized today, two in critical condition in the burn unit at the University of Utah Health Sciences Center in Salt Lake City. A teacher shot in the back was released from a hospital today.

Marlene Hess said the siege will leave its mark on the children of Cokeville, a southwestern Wyoming town of about 550 people. "They're just going to have to learn there are sick people in this world. It's something we're going to have to live with."

Mayor John Dayton said the people of this agricultural community are a "pretty tough bunch" who will cope with this hardship the way they cope with others. Winters are long and bitter in this part of Wyoming. Boarded shops along Cokeville's two main roads reflect the region's depressed economy.

Dayton said David Young, 42, operated a gun shop here about seven years ago while he was town marshal, a position he held for six months before being asked to resign. "We don't like to use the word 'fired' here," Dayton said.

Athalene Long, who lived in a nearby community when David Young was the marshal, said residents used to jokingly refer to him as "Wyatt Earp." She said he wore a wide-brimmed cowboy hat and carried a long-barreled pistol in a holster strapped to his leg, like an Old West gunfighter.

David Young met Doris Lydle, his future wife, in Cokeville. Lincoln County Sheriff T. Deb Wolfley said he has traced her to Idaho and Tucson, where a house trailer is registered in her name. David Young has been traced to law enforcement agencies that he worked for in Nebraska, Idaho and Wyoming.

Wolfley said two diaries and other printed material found among the Youngs' belongings in a Montpelier, Idaho, motel may help explain their motives. He said an entry Tuesday in Doris Young's diary speculated what they would do with the money and asked, " 'What will we be called in the new land?' What that means, I don't know."

There was speculation here today that the Youngs were associated with Posse Comitatus, a paramilitary group opposed to income taxes and other legal authority. The sheriff said he had seen nothing to persuade him that the Youngs were associated with the group.

The Youngs are believed to have arrived in the Cokeville area about May 13 with Doris' daughter Princess, 19; Gerald Deppe, 42, of Grinwell, Iowa; and Doyle Mendenhall, 31, of Preston, Idaho.

Deppe and Mendenhall have told investigators that David Young asked to meet them in the Cokeville area to discuss an unspecified business venture. They claim to have no idea the Youngs were planning to take pupils hostage. Princess Young said she, too, was unaware of the plan.

On Friday, the five spent several hours riding around Cokeville in a rented Toyota van as the Youngs explained their plans for taking over the school and demanding $2 million ransom for each child.

When Deppe and Mendenhall objected, officials said, David Young allegedly threatened them with an automatic rifle. He then handcuffed the men and ordered his stepdaughter to drive to the school and help unload the cache of explosives and weapons. David Young told her to drive away. The two handcuffed men were in the back seat.

She went directly to the Cokeville police station and told officials what was happening.

Meanwhile, David and Doris Young walked into the school and announced to secretary Christine Cook, "This is a revolution. We're taking this school hostage."

Witnesses said they rounded up students, teachers and administrators and threatened to set off the bomb if their demands, including a meeting with President Reagan, were not met.

One of the former hostages, watching today as agents from the Bureau of Alchohol Tobacco and Firearms gleaned evidence at the school, said the Youngs had been "kind of nice" to him and the others. "It was one of the boy's birthday and the man and the lady sang 'Happy Birthday' to him," said Rusty Birch, 10.

He said that soon after the songs were finished, he saw the woman in flames.

About two hours after the incident began, officials said, David Young handed the bomb's detonator to his wife and walked into an adjacent restroom. Doris Young apparently dropped or otherwise mishandled the detonator, setting it off.

In the chaos that followed, David Young fired a shot that struck music teacher John Miller in the back, then turned the gun on himself.

Spokesman John Dwan at the University of Utah Burn Clinic in Salt Lake City said Tina Morefield, 9, was in critical but stable condition today with burns over 12 percent of her body and Billie Joe Hutchinson, 7, was in serious condition with burns over 21 percent of her body.

A Logan, Utah, hospital reported that one adult and two children were in good condition. Seven children and an adult were hospitalized in Montpelier, Idaho, and two children were at a Kemmerer, Wyo., hospital in good condition